N.Y. Civil Practice Law & Rules § 3024 (2026)

Rule 3024. Motion to correct pleadings. (a) Vague or ambiguous
pleadings. If a pleading is so vague or ambiguous that a party cannot
reasonably be required to frame a response he may move for a more
definite statement.
  (b) Scandalous or prejudicial matter. A party may move to strike any
scandalous or prejudicial matter unnecessarily inserted in a pleading.
  (c) Time limits; pleading after disposition. A notice of motion under
this rule shall be served within twenty days after service of the
challenged pleading. If the motion is denied, the responsive pleading
shall be served within ten days after service of notice of entry of the
order and, if it is granted, an amended pleading complying with the
order shall be served within that time.