File locking.
Imagine a system that allows you to see a list of music available from your peers. If you stream a song from your peer, a file lock engages on their copy. That peer is unable to play the song. If they need to get to song, they could end the stream.
Such a system exactly mirrors sharing physical media. You are bereft of the item. You don't get the item back until the person to whom you lent the item returns it. Return occurs hen the file lock is relinquished. As such it should be perfectly legal to share.
The difficulty with such a system is that there is little place for profit. The software does provide a serivce: indexing and suggestions and playlists. You could do ads. People might not join because of it. You could charge a low flat fee. Just hard to monetize it.