Rzewski's De Profundis is perhaps the most famous example. It calls for recitation, singing, whistling, percussive effects, etc., all around a text by Oscar Wilde. Another, less known example is Brian Ferneyhough's Opus Contra Naturam, which calls for recitation, but it is not precisely coordinated with the music the way the Rzewski is. The pianist, according to the composer, is meant to recite the text as if they are having a conversation with the piano. An even less known work for recitation and piano is Walter Zimmerman's "When I'm 84", which calls for the pianist to count to 84 in Japanese while playing a very simple and delicate accompaniment. An even-LESS known piece (or rather set of pieces) are Brett Dean's Equality and Prayer, both for speaking pianist. They both set poems by Michael Leunig which are both quite striking, and I will admit, the piece Equality made me laugh out loud when I saw it performed. There are lots of piano pieces by George Crumb that call for noise making from the performers. Look at his various Makrokosmos series for some examples. My favorites from my list are the Rzewski and Dean works. The Ferneyhough has an incredibly difficult part, but the upside is that it calls for the pianist to dress up as a Liberace or Joker-like figure (it is actually part of an opera, but functions as a standalone piece also), which could be quite humorous in performance.
There are actually quite a bit of "theatrical" works for a speaking/noise-making pianist, for I once attended a recital largely made up of these works. I mentioned many of the works here. There were even a few pieces on that program by the pianist herself, Vicki Ray. Unfortunately, I haven't heard these works again, so I can't comment specifically on them, for they were not as distinctive as the ones I mentioned above.
Topic: Theatre Pieces