SELYA, Circuit Judge.

A cadre of former pilots for Eastern Airlines, Inc. (Eastern) brought an action under the Employee Retirement Income Security Act (ERISA), 29 U.S.C. § 1001 et seq. (1994), against the trustee of the failed air carrier’s retirement plan. The district court dismissed the suit after reviewing the trust agreement and concluding that the trustee was not subject to ERISA liability as a fiduciary or co-fiduciary in respect to the harms alleged. The plaintiffs appeal. We affirm.

I. BACKGROUND

We draw the facts from the plaintiffs’ complaint and the trust agreement. In 1958, Eastern and the union representing its pilots established a defined contribution retirement plan (the Plan) designed to provide retirees with a range of pension options. Almost a quarter-century later, the Plan’s administrative committee (the TAC) retained State Street Bank and Trust Company (the Bank) to hold the Plan’s assets in trust, manage them as directed, and periodically report their value (so that the TAC, inter alia, could effectuate the Plan by calculating annuity and lump-sum retirement benefits). The parties spelled out the Bank’s duties and obligations qua trustee in a trust agreement (the Agreement).

As time went by, the Plan invested heavily in real estate. In reporting the value of these investments, the Bank relied on information obtained from Hawthorne Associates, Inc. (Hawthorne), the Plan’s principal investment manager, in the form of periodic appraisals prepared by Blake, a consultant engaged by Hawthorne. Despite a subsequent decline in the real estate market, Blake assigned consistently high valuations to the Plan’s properties and the Bank parroted those valuations in its reports to the TAC.

■In the summer of 1991, the Bank expressed concern anent the figures supplied by Hawthorne. Eventually, it hired Spauld-ing & Slye (S & S), an independent appraisal firm, to review Blake’s handiwork. Upon encountering difficulty in gaining access to the necessary information, the Bank wrote to Hawthorne stating that:

Our appraiser is prepared to begin his review on Monday, October 7. If he is not permitted to begin his review by Friday, October 11 on the basis of full access to the documents, we believe that we have no recourse but to seek the advice of the Department of Labor as to our concerns about Hawthorne’s instructing us to continue to report the real estate at values supplied by Hawthorne as investment manager.

In short order, Hawthorne relented and an unencumbered review proceeded.

S & S thereafter issued a report that criticized Blake’s valuations and recommended that new appraisals be secured from a new appraiser. The Bank submitted the S & S report to the TAC on November 8,1991. One week later, the Bank wrote to the TAC’s attorney expressing concern that, according to S & S, “many of the appraisals are incomplete and/or suffer from methodological flaws.” The Bank declared that it was “unwilling to continue to carry these valuations on its books without qualification in light of the[se] concerns.” Within a matter of weeks, Hawthorne informed the Bank that it had lowered the appraised values of. certain properties. The Bank accepted the new figures without further investigation.

*16 The TAC eventually retained an independent appraiser to assess the Plan’s real estate holdings. This exercise culminated in a substantial reduction of the reported values. At that point, it became evident that Blake’s exaggerated valuations, had skewed the Plan’s finances: because inflated appraisal figures had been carried on the Plan’s books for nearly a decade, retiring pilots who opted for lump-sum.retirement benefits during that period received a windfall, whereas the remaining Plan participants were left holding an unduly depleted bag.

II. THE ENSUING LITIGATION

Eastern filed for bankruptcy in 1989. In due course, several quondam pilots brought an action in a Florida federal court against the Plan, its sponsors, the TAC, and sundry other parties (not including the Bank). The plaintiffs’ complaint invoked ERISA and alleged myriad breaches of fiduciary duty in connection with the investment of the Plan’s assets. See Beddall v. Eastern Air Lines, C.A. No. 91-1865-CIV (S.D.Fla.) (Beddall I). The Florida court transferred the case to Massachusetts. See 28 U.S.C. § 1404(a).

The Beddall I plaintiffs moved to amend the complaint to add the Bank as a defendant. As a precaution, they also initiated a separate suit against the Bank in the Massachusetts federal court {Beddall II). The complaint in the latter suit charged that the Bank violated ERISA’s fiduciary provisions by its failure to ensure that the Plan’s holdings were valued appropriately.

Judge Wolf eventually approved a class action settlement in Beddall I, see Beddall v. Eastern Airlines Variable Benefit Retirement Plan for Pilots, No. 93-12074 (D.Mass. Nov. 7, 1996) (order approving final settlement), 1 and the plaintiffs withdrew the pending motion to amend. The Bank then moved to dismiss Beddall II for failure to state a claim. See Fed.R.Civ.P. 12(b)(6). The district court granted the motion. See Beddall II v. State Street Bank & Trust, 1996 WL 74218 (D.Mass.1996). Judge Wolf concluded that, because the Agreement absolved the Bank of any fiduciary responsibility for the alleged overvaluation of the Plan’s real properties once the TAC engaged Hawthorne as the investment manager in respect to those asséts, the complaint failed to state an actionable ERISA claim for breach of fiduciary duty. See id at *l-*2. Then, citing ERISA § 405(d), 29 U.S.C. § 1105(d), the judge determined that, even if the Bank knew or should have known of Hawthorne’s indiscretions, co-fiduciary liability did not attach in the absence of an allegation that the Bank had participated actively in, or concealed, the breach. See id. at *2. This appeal ensued.

III. STANDARD OF REVIEW

We afford de novo review to a district court’s resolution of a motion to dismiss. See Garita Hotel Ltd. Partnership v. Ponce Fed. Bank, 958 F.2d 15, 17 (1st Cir.1992). Like the court below we must accept as true the factual allegations of the complaint, construe all reasonable inferences therefrom in favor of the plaintiffs, and determine whether the complaint, so read, limns facts sufficient to justify recovery on any cognizable theory of the case. See Dartmouth Review v. Dartmouth College, 889 F.2d 13, 16 (1st Cir.1989).

This is familiar lore. Here, however, there is an odd twist: the court below scrutinized not only the complaint but also the Agreement—and it is undisputed that the plaintiffs neither appended the latter document to the complaint nor incorporated it therein by an explicit reference. In this posture of the case, the lower court’s consideration of the Agreement gives us pause.

We think that this situation calls for a practical, commonsense approach—one that does not elevate form over substance. The complaint discusses the Agreement at considerable length. And, although it states con-clusorily that “State Street is a fiduciary of the Plan,” it then proceeds to summarize the parts of the Agreement that, in the plaintiffs’ view, justify this characterization. The Bank responded to these allegations by filing a Rule 12(b)(6) motion and appending to it a *17 copy of the Agreement. The plaintiffs neither challenged the authenticity of the Agreement nor moved to strike it from the record.

Under these circumstances, the Agreement was properly before the court. When, as now, a complaint’s factual allegations are expressly linked to—and admittedly dependent upon—a document (the authenticity of which is not challenged), that document effectively merges into the pleadings and the trial court can review it in deciding a motion to dismiss under Rule 12(b)(6). See Fudge v. Penthouse Int’l, Ltd., 840 F.2d 1012, 1015 (1st Cir.1988); see also Branch v. Tunnell, 14 F.3d 449, 454 (9th Cir.1994) (“[DJoeuments whose contents are alleged in a complaint and whose authenticity no party questions, but which are not physically attached to the pleading, may be considered in ruling on a Rule 12(b)(6) motion to dismiss.”); 2 James Wm. Moore et al., Moore’s Federal Practice § 12.34[2] (3d ed.1997) (explaining that courts may consider “[u]ndisputed documents alleged or referenced in the complaint” in deciding a motion to dismiss); see generally Fed.R.Civ.P. 10(c) (stating that “[a] copy of any written instrument which is an exhibit to a pleading is a part thereof’). Accordingly, we conclude that the district court had the authority to consider the Agreement if it chose to do so.

This conclusion makes eminent sense. A district court’s central task in evaluating a motion to dismiss is to determine whether the complaint alleges facts sufficient to state a cause of action. In conducting that tamis-age, the court need not accept a complaint’s “bald assertions” or “unsupportable conclusions.” Chongris v. Board of Appeals, 811 F.2d 36, 37 (1st Cir.1987). While a plaintiff only is obliged to make provable allegations, the court’s inquiry into the viability of those allegations should not be hamstrung simply because the plaintiff fails to append to the complaint the very document upon which by her own admission the allegations rest. Any other approach would seriously hinder recourse to Rule 12 motions, as a plaintiff could thwart the consideration of a critical document merely by omitting it from the complaint. We. doubt that the drafters of . the Civil Rules, who envisioned Rule 12(b)(6) motions as a swift, uncomplicated way to weed out plainly unmeritorious cases, would have countenanced such a result.

To their credit, the plaintiffs tacitly concede that the lower court had the prerogative to review the Agreement notwithstanding its omission from the complaint. They asseverate instead that the court should not have done so without also enabling them to submit other evidence (and, thereby, convert the motion before the court into one for summary judgment). We reject, that asseveration and hold that consideration of the Agreement did not in itself compel the court to treat the motion before it as one for summary judgment. 2 See Fed.R.Civ.P. 12(b). We offer three reasons in support of this ruling. First, the Agreement’s centrality to the plaintiffs’ contentions, as limned in their complaint, makes it in effect part of the pleadings, and, thus, differentiates its evaluation in conjunction with a motion to dismiss from the assessment of traditional extrinsic evidence. See Venture Assocs. Corp. v. Zenith Data Sys. Corp., 987 F.2d 429, 431 (7th Cir.1993) (“Documents that a defendant attaches to a motion to dismiss are considered a part of the pleadings if they are referred to in the plaintiff’s complaint and are central to her claim.”). Second, and relatedly, the complaint predicates the plaintiffs’ claims regarding the existence of the Bank’s ostensible fiduciary duties solely on the Agreement, not on external events. Lastly, the conversion of a Rule 12(b)(6) motion into a Rule 56 motion is a matter quintessentially within the purview of the district court’s sound discretion. See Garita Hotel, 958 F.2d at 18.

IV. ANALYSIS

We begin our treatment of the merits by examining the pertinent portions of ERISA’s *18 statutory scheme. We then turn to the plaintiffs’ triad of claims: (1) that the complaint states a cause of action for fiduciary liability by reason of the Bank’s discretionary authority over the Plan’s real estate holdings; (2) that the complaint states a claim for fiduciary liability arising out of the Bank’s conduct, including its role in respect to the Plan’s Short Term Investment Fund (the STIF); and (3) that the complaint states a claim against the Bank for co-fiduciary liability.

A. The Statutory Scheme.

ERISA’s fiduciary duty provisions not only describe who is a “fiduciary” or “co-fiduciary,” but also what activities constitute a breach of fiduciary duty. In the first instance, the statute reserves fiduciary liability for “named fiduciaries,” defined either as those individuals listed as fiduciaries in the plan documents or those who are otherwise identified as fiduciaries pursuant to a plan-specified procedure. 29 U.S.C. § 1102(a)(2). But the statute also extends fiduciary liability to functional fiduciaries—persons who act as fiduciaries (though not explicitly denominated as such) by performing at least one of several enumerated functions with respect to a plan. In this wise, the statute instructs that

a person is a fiduciary with respect to a plan to the extent (i) he exercises any discretionary authority or discretionary control respecting management of such plan or exercises any authority or control respecting management or disposition of its assets, (ii) he renders investment advice for a fee or other compensation, direct or indirect, with respect to any moneys or other property of such plan, or has any authority or responsibility to do so, or (iii) he has any discretionary authority or discretionary responsibility in the administration of such plan.

29 U.S.C. § 1002(21)(A).

The key determinant of whether a person qualifies as a functional fiduciary is whether that person exercises discretionary authority in respect to, or meaningful control over, an ERISA plan, its administration, or its assets (such as by rendering investment advice). See O’Toole v. Arlington Trust Co., 681 F.2d 94, 96 (1st Cir.1982); see also 29 C.F.R. § 2509.75-8, at 571 (1986). We make two points that inform the application of this rule. First, the mere exercise of physical control or the performance of mechanical administrative tasks generally is insufficient to confer fiduciary status. See Cottrill v. Sparrow, Johnson & Ursillo, Inc., 74 F.3d 20, 21-22 (1st Cir.1996); Concha v. London, 62 F.3d 1493, 1502 (9th Cir.1995), cert. dismissed, 517 U.S. 1183, 116 S.Ct. 1710, 134 L.Ed.2d 772 (1996). Second, fiduciary status is not an all or nothing proposition; the statutory language indicates that a person is a plan fiduciary only “to the extent” that he possesses or exercises the requisite discretion and control. 29 U.S.C. § 1002(21)(A). Because one’s fiduciary responsibility under ERISA is directly and solely attributable to his possession or exercise of discretionary authority, fiduciary liability arises in specific increments correlated to the vesting or performance of particular fiduciary functions in service of the plan, not in broad, general terms. See Maniace v. Commerce Bank, 40 F.3d 264, 267 (8th Cir.1994); Brandt v. Grounds, 687 F.2d 895, 897 (7th Cir.1982); NARDA, Inc. v. Rhode Island Hosp. Trust Nat’l Bank, 744 F.Supp. 685, 690 (D.Md.1990).

An ERISA fiduciary, properly identified, must employ within the defined domain “the care, skill, prudence, and diligence under the circumstances then prevailing that a prudent man acting in a like capacity and familiar with such matters would use.” 29 U.S.C. § 1104(a)(1)(B). The fiduciary should act “solely in the interest of the participants and beneficiaries,” and his overarching purpose should be to “provid[e] benefits to the participants and their beneficiaries” and to “defray[] reasonable expenses of administering the plan.” Id. § 1104(a)(1). A fiduciary who fails to fulfill these responsibilities is “personally liable to make good to [the] plan any losses to the plan resulting from ... such breach.” Id. § 1109(a).

Co-fiduciary liability is a shorthand rubric under which one ERISA fiduciary may be liable for the failings of another fiduciary. Co-fiduciary liability inheres if a fiduciary *19 knowingly participates in or conceals another fiduciary’s breach, enables such other to commit a breach, or learns about such a breach and fails to make reasonable efforts to remedy it. See id. § 1105(a). In some circumstances, co-fiduciary liability is subject to a special set of rules. This is true, for example, where the putative co-fiduciary is a trustee and the breach is at the hands of a plan-appointed investment manager. See id. § 1105(d)(1) (stating generally that a trustee shall only be liable for a money manager’s violation if the former participates in or acts to conceal the breach).

B. The Bank’s Status.

The starting point for reasoned analysis of the Bank’s fiduciary status is the Agreement. In support of their assertion that the Bank bears fiduciary responsibility for Hawthorne’s misvaluation of the real estate investments, the plaintiffs direct our attention to three sections of the Agreement, which we set out in pertinent part:

Section 3. Investment of the Fund. The Trustee [the Bank] shall cause all principal and income at any time forming a part of the fund to be invested as a single fond, ... in such property as the Trustee may deem proper and appropriate____

Section 4. Duties and Powers of the Trustee. The Trustee [the Bank] shall have the duties, powers and responsibilities with respect to the Fund, in addition to and not in modification or limitation of the authority provided by law and this Agreement:

(a) to manage, control and operate the Fund and to prepare and submit to the Committee [the TAC] and Eastern, and otherwise as required by applicable law, all financial information, including periodic valuation of the Fund, as required by law, the Plan and this Agreement;

(c) to invest and reinvest the Fund, as provided in Section 3 of this Agreement;

Section 5. Records, Accounting and Valuation of the Assets of Fund. The Trustee [the Bank] shall keep accurate accounts of all investments, receipts and disbursements and other transactions hereunder regarding the Fund____

Following the close of each month the Trustee shall provide the Committee [the TAC] and Eastern and such others as they shall direct from time to time with a monthly report of the assets held in the Fund as of the close of said month____

Except as otherwise provided in this Section, the assets of the Trust at any monthly or annual valuation date shall be valued at market value as of such date____ Real property .,. shall be valued at market value on the valuation dates on the basis of information obtained from qualified, available sources such as dealers, bankers, brokers, or appraisers dealing or familiar with the type of investment involved, or on the basis of reference to the market value of similar investments; and the Trustee may rely on an appraisal of real property made by an independent appraiser deemed competent by the Trustee, within two years prior to the valuation date as of which such value is being determined.

We also deem relevant to the Bank’s status as regards real estate investments another section of the Agreement that the plaintiffs tend to downplay. We reprint that provision in pertinent part:

Section 6. Appointment of Investment Manager. The Committee [the TAC] ... may direct the Trustee [the Bank] in writing to segregate all or a portion of the Fund, including without limitation, all or a portion of such investments as may be initially transferred to the Trustee in accordance with this Agreement, into one or more separate accounts to be known as “Investment Manager Accounts.” ... The Committee shall promptly thereafter appoint for each Investment Manager Account an Investment Manager ... and shall give written notice of such appointment to the Trustee____

It shall be the responsibility of the Committee to vest each Investment Manager with the authority necessary to discharge *20 its duties hereunder and to properly direct each Investment Manager to perform such accounting and valuation functions and such other duties as shall be necessary to enable the Trustee to fully perform- hereunder..

The Trustee shall follow the directions of each Investment Manager with respect to the Investment Manager Account forming part of the Fund; provided that all such directions be in writing, signed by an officer, or partner, of such Investment Manag-er____ The Trustee shall have no obligation to act pursuant to any directions from any Investment Manager unless and until it receives such directions in a form satisfactory to it.

The Trustee shall have no responsibility for supervising any Investment Manager. The Trustee shall be under no obligation to invest or otherwise to manage any asset of the Fund which is subject to the management of any Investment Manager. The Trustee shall be under no obligation to review or to make inquiries as to any action or direction of any Investment Manager taken as provided herein or as to any failure to give directions, nor to review or value the assets held in any Investment Manager Account, nor to make any suggestions to the Investment' Managér or Committee or Eastern with respect to the investment and reinvestment of, or disposal of investments in, any Investment Manager Account____■ The Trustee shall not be liable for any act or omission of any Investment Manager, except as provided in Section 405(a) of ERISA [29 U.S.C. § 1105(a)],

In the case of any purchase or sale of real property by any Investment Manager, the Trustee shall have the right to request, as a condition to its executing any documents or paying over any assets of the Fund in connection with such transaction, that it receive a certified appraisal of the value of such property____

The plaintiffs read these provisions, in the aggregate, as conferring upon the Bank sufficient authority to make it a fiduciary in regard to the Plan’s real estate investments. We do not agree. The quoted-text authorizes the Bank mainly to perform administrative and ministerial functions - in respect to those investments which, like real estate, are held within a so-called Investment Manager Account. Without more, mechanical administrative responsibilities (such as retaining the assets and keeping a record of their value) are insufficient to ground a claim of fiduciary status. See O’Toole, 681 F.2d at 96 (concluding that a bank’s duties “as the depository for the funds do not include the discretionary, advisory activities described by the [ERISA] statute”); Pension Fund-Mid Jersey Trucking Indus.—Local 701 v. Omni Funding Group, 731 F.Supp. 161, 174-75 (D.N.J.1990) (similar).

To give the devil his due, we acknowledge that section 4, standing alone, might be construed as authorizing the Bank, under some circumstances, to manage the Plan’s real estate investments in a manner that would render it a fiduciary with regard to the valuation of those assets. Nevertheless, section 4 cannot be read in a vacuum. The TAC nominated Hawthorne as an investment manager. in respect to. the Plan’s real estate holdings, and the plain language of section 6 of the Agreement leaves little doubt but that the TAC thereby relieved the Bank of all fiduciary responsibility regarding those investments. In terms, section 6 shifts to an appointed investment manager all discretion over affected assets and makes the investment manager—not -the trustee—responsible for “perforating] such accounting and valuation functions and such other duties as shall be necessary to enable the Trustee to fiilly perform.” To cinch matters, section 6 expressly absolves the trustee of “responsibility for supervising any Investment Manager”; confirms that the trustee is not obliged “to review or make inquiries as to any action or direction of any Investment Manager,” or “to review or value the assets held in any Investment Manager account.” Further, it proclaims, with a single exception not relevant to this discussion, that the trustee “shall not be liable for-any act or omission of any Investment Manager.” These stipulations strip any veneer of plausibility from the plaintiffs’ bald assertion that the Bank is a fiduciary subject to liability for Hawthorne’s overvaluation pf the Plan’s real property.

*21 In a last-ditch attempt to blunt the force of this conclusion, the plaintiffs point to language that gives the trustee the right to reject the investment manager’s directions in certain circumstances—say, if those directions are not “in a form satisfactory to it”—and they argue that, as a result of this “discretion” (to use plaintiffs’ word), the Bank retains its status as a fiduciary notwithstanding the other language contained in section 6. This argument will not fly.

It is beyond cavil that when the TAC appoints an investment manager for designated assets, the Agreement shifts all significant discretion and control over those assets to the investment manager and relegates the trustee to the role of an administrative functionary. With section 6 velivolant, the Bank’s remaining powers are ministerial. They involve such details as checking whether Hawthorne’s instructions are in a writing signed by an authorized person and issuing periodic reports to the TAC anent the Fund’s status. Although the Bank arguably may refuse to follow instructions that are not in an acceptable format, this negative discretion lies well within the administrative sphere, and its existence does not transform the Bank into a fiduciary vis-a-vis the affected assets. 3 See Arizona State Carpenters Pension Trust Fund v. Citibank, 125 F.3d 715, 722 (9th Cir.1997).

We need not paint the lily. The complaint acknowledges that the TAC appointed Hawthorne to manage its real estate investments. In that circumstance, the trust document, read as a whole, divests the Bank of any and all management authority or discretionary control over those assets. Whatever the Bank’s powers may have been in the absence of a duly appointed investment manager, no fiduciary responsibility in regard to the valuation of the Plan’s real estate-holdings survived the appointment.

C. The Bank’s Actions.

Charting a slightly different flight path, the plaintiffs urge us to set the Agreement to one side and to deem the Bank a fiduciary of the Plan’s real estate investments by virtue of its actions. They posit that, because the Bank was not entirely passive—it questioned Hawthorne’s valuations, engaged an independent appraiser to review Hawthorne’s numbers, and ultimately threatened to report Hawthorne’s practices to the authorities—it acted as a fiduciary and thus we should treat it as one. We think not.

As a matter of policy and principle, ERISA does not impose Good Samaritan liability. A financial institution cannot be deemed to have volunteered itself as a fiduciary simply because it undertakes reporting responsibilities that exceed its official mandate. Imputing fiduciary status to those who gratuitously assist a plan’s administrators is undesirable in -a variety of ways, and ERISA’s somewhat narrow fiduciary provisions are designed to avoid such incremental costs. See generally Mertens v. Hewitt As socs., 508 U.S. 248, 262-63, 113 S.Ct. 2063, 2071-72, 124 L.Ed.2d 161 (1993). Viewed against this backdrop, a rule that would dampen any incentive on the part of depository institutions voluntarily to make relevant information available to fund administrators and other interested parties is counter-intuitive. Moreover, such a wrong-headed rule “would also risk creating a climate in which depository institutions would routinely increase their fees to account for the risk that fiduciary liability might attach to nonfiduciary work;” Arizona State Carpenters, .125 F.3d at 722.

To the extent that the plaintiffs’ fiduciary claim derives from the Bank’s activities with regard to Plan assets apart from real estate, it fares no better. The plaintiffs argue that because the Bank is a fiduciary with regard to the STIF, it had a statutory responsibility to make a timely disclosure to the Plan participants of its concerns about Hawthorne’s real estate valuations. We agree with the plaintiffs’ premise—clearly, the Bank had some discretion with regard to *22 investing cash in the STIF—but their conclusion does not necessarily follow.

Refined to bare essence, the question is whether an ERISA fiduciary for one purpose has an obligation to disclose his suspicions even when there is no nexus between his particular fiduciary responsibilities and the perceived jeopardy. This is an issue of first impression, certainly in this circuit, and perhaps more broadly. Good arguments exist on both sides. On the one hand, the obligations of an ERISA fiduciary, while governed by federal law, are informed by the common law of trusts. That law generally treats the communication' of material facts to the beneficiary as “the core of a fiduciary’s responsibility.” Eddy v. Colonial Life Ins. Co., 919 F.2d 747, 750 (D.C.Cir.1990). 4 On the other hand, it is settled that a non-fiduciary’s failure to communicate knowledge of a fiduciary’s breach does not “constitute culpable participation in a breach of trust under ERISA.” Painters of Philadelphia Dist. Council No. 21 Welfare Fund v. Price Waterhouse, 879 F.2d 1146, 1153 n. 9 (3d Cir.1989).

Although this question is both close and interesting, we need not answer it today. Apart from the co-fiduciary claim, considered infra, the plaintiffs’ complaint does not premise a claim on the Bank’s supposed obligation to inform Plan' participants of the suspected misvaluations. Instead, the complaint predicates the plaintiffs’ alternate claim of fiduciary liability on the Bank’s “willingness to accept Hawthorne’s instructions as to the values to be carried on [the Bank’s] books.” According to the complaint, this gaffe “resulted in those properties being carried on the [Bank’s] books for many years at values greatly in excess of their market values, which in turn led to retiring pilots receiving millions more in lump sum benefits than the benefits to which they were entitled.” Nowhere in the complaint (or in the plaintiffs’ opposition to the motion to dismiss, for that matter) do the plaintiffs make the entirely distinct claim that the Bank breached a fiduciary obligation under ERISA because it failed to notify Plan participants of Hawthorne’s erroneous appraisals.

That ends the matter. Afterthought theories—even cleverly constructed afterthought theories—cannot be introduced for the first time in an appellate venue through the simple expedient of dressing them up to look like preexisting claims. “If any principle is settled in this circuit, it is that, absent the most extraordinary circumstances, legal theories not raised squarely in the lower court cannot be broached for the first time on appeal.” Teamsters Local No. 59 v. Superline Transp. Co., 953 F.2d 17, 21 (1st Cir.1992); accord McCoy v. M.I.T., 950 F.2d 13, 22 (1st Cir.1991). Since there are no extraordinary circumstances here—when the plaintiffs sued, they had experienced counsel, a good grasp of the facts (honed by the rigors of Beddall I), and ample time to decide which arguments to press—that principle applies full bore.

D. Co-Fiduciary Liability.

The plaintiffs’ final approach centers around a. claim that the Bank is liable as a co-fiduciary. This claim comes perilously close to suffering from the same procedural infirmity that we have just identified. The complaint is not artfully pleaded and no explicit co-fiduciary liability claim appears on its face. Nevertheless, the plaintiffs argued a co-fiduciary liability claim theory below and the district court addressed it. 5 So do we.

*23 We need not linger long. The short of it is that the plaintiffs’ allegations, even if well-pleaded and assumed to be true, do not establish a violation of ERISA’s co-fiduciary provisions. ERISA renders a fiduciary vulnerable to liability for breaches committed by other fiduciaries in three situations:

(1) if he participates knowingly in, or knowingly undertakes to conceal, an act or omission of such other fiduciary, knowing such act or omission is a breach;

(2) if, by his failure to comply with ... the administration of his specific responsibilities which give rise to his status as a fiduciary, he has enabled such other fiduciary to commit a breach; or

(3) if he has knowledge of a breach by such other fiduciary, unless he makes reasonable efforts under the circumstances to remedy the breach.

29 U.S.C. § 1105(a). Given their allegations, the plaintiffs’ claim miist stand or fall on the third of these scenarios. 6 We think that it falls.

29 U.S.C. § 1105(d) provides that a fiduciary (such as the Bank) cannot be held responsible as a co-fiduciary on the basis of acts described in section 1105(a)(2) or (3):

If an investment manager or managers have been appointed ... then, notwithstanding subsections (a)(2) and (3) ..., no trustee shall be liable from the acts or omissions of such investment manager or managers, or be under an obligation to invest or otherwise manage any asset of the plan which is subject to the management of such investment manager.

29 U.S.C. § 1105(d) (emphasis supplied). Given its literal meaning, section 1105(d) de-fenestrates-the plaintiffs’ claim that the Bank is subject to co-fiduciary liability in this instance.

The plaintiffs attempt to steer away from the obvious conclusion and to ensure a soft landing by two stratagems. First, they point to the exact language of section 6 of the Agreement (“The Trustee shall not be liable for any act or omission of the Investment Manager, except as provided in Section m(a) of ERISA [29 U.S.C. § 1105(a) ].”) (emphasis supplied). This verbiage, they assert, evinces an intent to hold a fiduciary liable for all the conduct described in section 1105(a), without reference to the exculpatory provisions of section 1105(d). We reject that assertion out of hand. The Agreement’s reference to 29 U.S.C. § 1105(a) can only be read as incorporating that section to the extent that it would impart liability under the statute. Cf Chicago Bd. Options Exchange, Inc. v. Connecticut Gen. Life Ins. Co., 713 F.2d 254, 259 (7th Cir.1983) (stating that “although the parties may decide how much authority to vest in any person, they may not decide how much [ERISÁ] liability.attaches to the exercise of that authority”).

The plaintiffs’ second attempt to avoid the clear implication of section 1105(d) is disingenuous at best. They speculate that Hawthorne may not be an “investment manager” within the meaning of the statute. This suggestion contradicts the premise on which the case has been argued up to this point and is thus precluded. In the district court, the plaintiffs repeatedly characterized Hawthorne as the Plan’s “principal money manager,” and never contended otherwise during the hearing on the motion to dismiss. The plaintiffs must have recognized that the district court understood their representations to be an admission that Hawthorne was an investment manager (at least for the purpose of the pending Rule 12(b)(6) motion). Moreover, the plaintiffs made no effort to correct the district court’s understanding by moving for reconsideration after Judge Wolf had issued his decision. See, e.g., VanHaaren v. State Farm Mut. Auto. Ins. Co., 989 F.2d 1, 4-5 (1st Cir.1993). We generally will not permit litigants to assert contradictory positions at different stages of a lawsuit in order to advance their interests. See Patriot Cinemas, Inc. v. General Cinema Corp., 834 F.2d 208, 211-12 (1st Cir.1987); see also United States v. Levasseur, 846 F.2d 786, 792-93 (1st Cir.1988) (stating the rule but *24 finding exceptional circumstances sufficient to warrant a departure). In all events, even if the investment manager gambit is not judicially estopped, it is surely waived inasmuch as it makes its debut in this court.

V. CONCLUSION

We need go no further. Because the trust agreement (coupled with the TAC’s appointment of Hawthorne) unambiguously establishes that the Bank retained no discretionary authority over the Plan’s real estate investments, we hold that the complaint fails to state an actionable claim against the Bank for Hawthorne’s overvaluation of those assets. By the same token, the complaint fails to state an actionable claim for co-fiduciary liability inasmuch as ERISA, specifically 29 U.S.C. § 1105(d), limits such liability to knowing participation or concealment—• facts not alleged in this ease. Hence, the district court appropriately granted the Bank’s motion to dismiss.

Affirmed.

. Under the settlement, the named defendants paid the Plan more than $10,000,000. As a condition of the settlement, Judge Wolf. precluded the Bank from impleading any of the settling defendants in the instant action.

. There is a certain irony to the plaintiffs’ criticism of the district court’s course of action. Although the conversion of the plaintiffs’ motion would have enabled them to submit evidence regarding the Bank's fiduciary responsibilities, the act of conversion also would have imported the summary judgment standard into the case and raised the bar for the plaintiffs. See Fed. R.Civ.P. 12(b). By eschewing conversion, the district court ensured that the plaintiffs’ complaint would be subjected to the less demanding scrutiny associated with motions to dismiss.

. Similarly, the Bank’s retention under section 6 of a right to secure a certified appraisal of the real estate does not alter the decisional calculus because the Bank has no such duty. Indeed, section 6 explicitly provides that the Bank has no obligation "to review or value the assets held in any Investment Manager Account.”

. We note, however, that the Eddy court described ERISA's fiduciary duty to disclose as the duty “not only to inform a beneficiary of new and relevant information as it arises, but also to advise him of circumstances that threaten interests relevant to the relationship." Eddy, 919 F.2d at 750 (emphasis supplied). Indeed, every case that the plaintiffs have cited in support of an affirmative duty to disclose arises in a context in which the plaintiff charges the defendant with withholding information related (i.e., relevant) to the fiduciary’s association with the plan. See, e.g., Ream v. Frey, 107 F.3d 147, 149-50 (3d Cir.1997); Glaziers and Glassworkers Union Local No. 252 Annuity Fund v. Newbridge Sec., Inc., 93 F.3d 1171, 1175-77 (3d Cir.1996).

. The lower court apparently cobbled the co-fiduciaiy claim together from a liberal reading of the complaint. The complaint does allege that the Bank is a fiduciary (an allegation that is irrefutable with regard to the STIF), that it had some knowledge of Hawthorne’s improprieties, and that it failed to make reasonable efforts to remedy the situation.

. Of course, the Bank argues that it did, indeed, take reasonable steps to investigate Hawthorne's improprieties and put an end to them. The potential issues relating to whether such steps actually were taken and/or their sufficiency are not before us, and we do not endeavor to decide those issues.