Other movies like this?

Um... Nine. Burlesque. The Producers. Cabaret. Hairspray. Victor Victoria. Evita. The Great Gatsby. Paris 36. Top Hat. Mrs Henderson Presents. All That Jazz. Gentlemen Prefer Blondes. Mamma Mia...

There are really very few movies that are comparable to these two so I'm just spitting out whatever comes to mind lol. The best movies of those I suggested are definitely: Victor Victoria, Top Hat, The Producers, and Gentlemen Prefer Blondes. Try those. :) Visually, they are not comparable but they are excellent.

All About Eve (1950)
Death Becomes Her (1992)
Showgirls (1995)
Wild Things (1998)
8 femmes (2002)

I strongly suggest Francis Ford Coppola's "The Cotton Club" (1984), which has a lot in common with "Chicago" but is more realistic, less sarcastic and contains far less musical pieces. I'm surprised no one has mentioned it yet.