(a) Any party claiming a preference under CPLR 3403 may apply to the court in the manner prescribed by that rule, the note of issue therein referred to being deemed a reference to a notice of trial.

(b) Counterclaims and cross-claims.

A counterclaim or cross-claim which is not entitled to a preference shall not itself defeat the plaintiff's right to a preference under this section.

(c) Result of preference being granted.

If a preference is granted, the action shall be placed ahead of all nonpreferred pending cases, as directed by the court, unless the court otherwise orders.