This Schubert Dance (Op 33, D. 783, No. 10), available in the Dover book "Schubert Dances," seems to be suitable for endless improvisation.
You could play it with ice tongs and it would still sound good.
Playing through these, I started putting smiley faces by the ones I liked immediately or thought otherwise admirable in some way. About a year later Cole asked, "Why do they all have smiley faces?"
I said, they don't; just the ones I like. But then he challenged me to find one that didn't have the smiley. Not so easy.
From the archives (Jan 2002): I tried to compose a Schubert Waltz.