This would also tie into improvisation and ear training, I'm wondering how I might structure a program which would teach students to hear and anticipate harmonic progression while improvising a melody. Students are often not even aware that there are choices about how to move through harmonic sequences. Perhaps taking a famous piece and recomposing it. Fur Elise, for example.
One very gifted student I taught did this naturally, he was always rearranging pieces or hearing new progressions and relations to other pieces. He would add his own coda's, and change the key to minor and so on. He had a riot doing this adding his Elvis ending to a piece of Beethoven, or improvise Chopin in the style of the Bee Gees, very inventive kid. A lot of it was just silly playing around, but my point is that he did in fact hear alternative ways to do things, and it would seem that it is always this process of 'hearing' which takes us deeper into a piece, or an improvisation, or issues to do with technique and theory for example.