Kiss Me, Kate is the 1953 MGM film adaptation of the Broadway musical of the same name.
Inspired by The Taming of the Shrew, it tells the tale of musical theater actors, Fred Graham and Lilli Vanessi, who were once married and are now performing opposite each other in the roles of Petruchio and Katherine in a Broadway-bound musical version of William Shakespeare's play.
Already on poor terms, the pair begin an all-out emotional war mid-performance that threatens the production's success. The only thing keeping the show together are threats from a pair of gangsters, who have come to collect a gambling debt from the show's Lucentio, Bill Calhoun. In classic musical comedy fashion, slapstick madness ensues before everything is resolved. --Wiki