I think that if you treat "What Do You Do With A BA in English" as its own song, instead of part of an opening sequence that leads us to "It Sucks To Be Me," you might count that.
One version of The Baker's Wife started with a French folk-ish guitar/vocal thing called "Bienvenue A Concorde," sung by a minor character, that really added nothing to the show (except time) - starting straight off with "Chanson" was a much smarter choice.
There's that bit of guitar/vocal "Este fuego" which opens Man Of La Mancha, though it seems as if this was added at some point and not yet set in the show at the beginning of its run. (It was not in the first printing of the score, then added for the revised score which is what is published now. It may be that it was something improvised, then later set.)
The Will Rogers Follies opens with that introductory chorus of "Let's Go Flying," though "Will-A-Mania" feels like the real opening. Similar in Kinky Boots with the Price and Son Theme followed by "The Most Beautiful Thing In The World."
Somewhat ironic that the song "K-ra-zy For You" is, IMO, a (very) weak throwaway number at the start of Crazy For You, never heard again after that (except in some incidental moments). "I Can't Be Bothered Now" feels more like the opening number. |