When you buy music and listen to it, again and again, you will always hear the same one, without any variation. Live music at concerts is always a little different from the recorded version and also from live performance to live performance.
Have different versions recorded for each piece of music (in studio, live performances, both.) When you buy the music (for download or streaming) you get access to all the versions. You can choose which version to listen to at any given time, or let the software decide randomly or based on your previous behavior. A new digital format can also be created where you can break down the elements of the music so that the performer can record alternative elements for individual parts and they can be dynamically exchanged or added when you play the music.