Legal Question in Civil Litigation in New York

No.

First of all, you say you made a cross-claim against the plaintiff. WRONG MOVE.

CPLR 3011 provides:

There shall be a complaint and an answer.

An answer may include a counterclaim against a plaintiff and a

cross-claim against a defendant. A defendant's pleading against another

claimant is an interpleader complaint, or against any other person not

already a party is a third-party complaint. There shall be a reply to a

counterclaim denominated as such, an answer to an interpleader complaint

or third-party complaint, and an answer to a cross-claim that contains a

demand for an answer. If no demand is made, the cross-claim shall be

deemed denied or avoided. There shall be no other pleading unless the

court orders otherwise.

So if you denominated your pleading as "Answer" or "Answer with Cross-Claim" then you waived a reply and the pleading is deemed denied. And I know of no surer way to make the judge dislike you than trying to turn a technical mistake into a victory. The judge will punish you for wasting her time. Stick to the merits or go home.