A party may amend a pleading, by leave of court, at any time, before or after judgment, so as to conform the pleading to the evidence. Applications to amend pleadings are within the sound discretion of the court, and leave shall be freely given upon such terms as may be just, even if the amendment substantially alters the theory of recovery.
Americore Drilling & Cutting, Inc. v. EMB Contr. Corp., NY Slip Op 05845 (2d Dep't October 27, 2021)