Of the ones in the past 20 years the musicals based on movies that have music at their center have fared best: The Producers Hairspray Once Kinky Boots The Band’s Visit Billy Elliott (although I wish the music had more of a punk sound) The School Of Rock (although the book was pretty much Mike White’s screenplay and the most memorable songs came from the film or were Amazing Grace)
Some shows did a fine job blending in songs while following a movie’s non-musical plot: Waitress A Gentleman’s Guide to Love and Murder
And Tootsie did a good job changing the movie’s milieu and story to create something new while building on the movie’s original vision.