N.Y. CVP Law § 2215

Rule 2215. Relief demanded by other than moving party. At least three\ndays prior to the time at which the motion is noticed to be heard, or\nseven days prior to such time if demand is properly made pursuant to\nsubdivision (b) of rule 2214, a party may serve upon the moving party a\nnotice of cross-motion demanding relief, with or without supporting\npapers; provided, however, that:\n (a) if such notice and any supporting papers are served by mailing, as\nprovided in paragraph two of subdivision (b) of rule 2103, they shall be\nserved three days earlier than as prescribed in this rule; and\n (b) if served by overnight delivery, as provided in paragraph six of\nsubdivision (b) of rule 2103, they shall be served one day earlier than\nas prescribed in this rule. Relief in the alternative or of several\ndifferent types may be demanded; relief need not be responsive to that\ndemanded by the moving party.\n