N.Y. Comp. Codes R. & Regs. tit. 9, § 465.4
(d) Any amendments made after a probable cause determination are not subject to any further investigations or determinations of probable cause.
(e) Service.
(a) Power to amend.
The division or the complainant shall have the power reasonably and fairly to amend the complaint. No party may be removed by any amendment. After a hearing is commenced before an administrative law judge, any amendment is subject to the discretion of the administrative law judge.
(b) Complainant's power.
The complainant has the right to amend the complaint in a reasonable manner before the commencement of a hearing.
(c) Division's power.
The regional director, division attorney, or administrative law judge may reasonably amend the complaint.