You may also want to investigate Smart Copies of songs, wherein the main song has backing tracks appropriate for band A, and a Smart Copy B has a backing track for band B, another Smart Copy C for band C, etc. (In this use case the Smart Copies inherit all the data from the main song (including future edits) except for the different backing track, making them easy to maintain.)
Create master 'picker' set lists of only the main songs, another with only Smart Copies for band B, another with only Smart Copies for band C, and so forth.
When creating a gig set list for a given band and when selecting songs, restrict your choices to the appropriate 'picker' set list (using the 'Add songs from:' option at the bottom of the pick list if using the web app).
(We use this method to manage alternative backing tracks that are gig-dependent)