Re Jack's post: we have a friend who plays Northumbrian pipes: he can play with a G or an F chanter, and he has a number of sets in each key (as you can imagine, G is more popular with the rest of assembled company!) But he can suggest a whole set in keys which suit him, and others are happy to go with that.
And going back to playing left hand with a B/C accordion, I was at a very nice workshop this last weekend, and played a lot of left hand along with the tunes, which were mainly in G or D majors, or Em or Am. We were playing from sheet music, and there were some Bms and F#ms, which I don't have chords for, but I can at least play a bass note that is part of the chord, e.g D for Bm or A for F#M.