It's almost impossible. In fact, without very sophisticated computer software, I would go so far as to say it is impossible. A recording, after all, is a record of the sound which is present in the space -- and pays no attention at all to what was making the sound.
If you had access to an original multi-track master, which had the piano on one track in its own space and the rest of the band on other tracks in their own spaces... such things happen with popular music (it's not uncommon for different bits of the band, never mind the vocals, to be recorded each in its own space -- sometimes in places miles apart on different days) but not, I think most classical music.