After "The Full Monty" film was released in 1997, there was some international confusion over the phrase, which it was taken as a euphemism for stripping. However, "the full Monty" now usually refers to taking something as far as it can go, similar to "the whole nine yards."
"The full Monty" historically refers to an old tailor called Sir Montague Burton. Going "the full Monty" meant purchasing a full three-piece suit, a shirt, and all of the trimmings.
"Our Christmas dinner had everything from sprouts to Yorkshire puddings. If you're going to have a roast, have the full Monty!"