The Venezuelan-born pianist Gabriela Montero is on a German tour and plays in Duesseldorf next Tuesday. She plays chestnuts from the Romantic repertory, as well as improvisations on themes from the classical repertoire.
You can submit a request for an improvisation on a particular theme on Montero’s Venezuelan-looking website here (warning: it will play her improvisations on Bach’s Italian Concerto as soon as you visit it). The improvisations are fully harmonized, sometimes a bit anachronistic (jazzy), and often damn pretty. It may sounds like a gimmick, but it was standard practice in Bach’s day — in fact, Bach’s spine-tingling ability to improvise on his own and others’ themes helped him get many of his posts.
I’m thinking of submitting a request for improvisation on the Sex Pistols’ "No Feelings," (the lawyers’ anthem). On second thought, what about John Cage’s 4:33?