CPLR § 4102

CPLR § 4102 Demand and waiver of trial by jury; specification of issues

(e) Relief by court.
The court may relieve a party from the effect of failing to comply with
this section if no undue prejudice to the rights of another party would
result.

Caruso, Caruso & Branda, P.C. v Hirsch, 2009 NY Slip Op 02314 (App. Div., 2nd, 2009)

The Supreme Court did not improvidently exercise its discretion in
denying the defendant's motion pursuant to CPLR 4102(e) for leave to
serve and file a late demand for a jury trial. A motion for such relief
must be based upon a factual showing that the earlier waiver of that
right was the result of either inadvertence or other excusable conduct
indicating a lack of intention to waive such a right (see Fischer v RWSP Realty, LLC, 53 AD3d 595, 597; Sumba v Sampaio, 44 AD3d 648; Hyatte v G.B.W. Glenwood Dental Admrs, Inc., 8 AD3d 233). The defendant failed to make such a factual showing (see Matter of Bosco, 141 AD2d 639).