N.Y. Comp. Codes R. & Regs. tit. 4 § 55.2
A committee on appeals shall consider only such appeals as clearly demonstrate a manifest material error or mistake appearing in a rating key or scale or in the application of such key or scale to candidate test papers or other records of examination performance or eligibility for appointment and only if such error or mistake affects the eligibility or relative standing of candidates. Further, the committee on appeals shall not consider the appeal of a candidate whose score, at the time of the establishment of the eligible list, is equal to or higher than the final examination rating of the third highest standing eligible. Provided, however, that the committee shall consider such appeal where the candidate's reachability for appointment is affected by the committee's determination of another appeal and he or she has timely filed a notice of intent to appeal.
N.Y. Comp. Codes R. & Regs. Tit. 4 § 55.2