Except--there is quite a bit in Moonstruck about public persona versus private persona, about the pressure to conform and the awareness of the expectations of others, often literally embodied by other people in the scene. The proposal in the restaurant, the rant in the deli, the date at the met, the tossing of the drink into the man's face in the restaurant--even the Aunt and Uncle and their clientele ("you were a tiger last night") and the grandfather with his group of friends. There is not only room for a chorus, there is reason. At the very least, they can function as the chorus does in The Light in the Piazza or Adding Machine or Here Lies Love.
Also, there are some wonderful moments for secondary characters in the published Shanley script for the movie--Nada Despotovich's character has some additional arc that could be exploited for the musical.
I am among those, however, that find the movie nearly perfect. It would have to be done with great care to please many that hold it near and dear.