Anything can try to squeeze a sequel out of it, and plenty of comedy/family books and movies that have done this.
Legally Blonde, Ace Ventura, Dumb and Dumber, Bring It On, The Hangover, Shrek, Alvin and the Chipmunks, American Pie, Bill & Ted, Step Up...I'm sure there are many, many more examples that aren't action movies. You can try to turn anything into a franchise.
I would also guess that horror films have produced more sequels than action movies.
Think about stuff like Anne of Green Gables and Little House on the Prairie. Those aren't detective or action based either.
The biggest problem with a stage sequel, for me, is that there is usually no dramatic reason for us to revisit the characters. Unless something is conceived as a trilogy or series of plays, a sequel feels tacked on, unnecessary and usually hilariously absurd.
Marie: Don't be in such a hurry about that pretty little chippy in Frisco.
Tony: Eh, she's a no chip!