With a bit of planning you can achieve what you want with overlayfs.
You would take all the files common to all instances and put them into the normally read-only lower directory.
Then, user overlayfs to mount a separate upper directory over the top of it for each differently modifiable copy you want. The upper directory can be empty to begin with meaning that each person just what's in the lower directory unmodified.
When an existing file is modified in any mounted overlay, it causes the file to be copied to the upper directory and overlay it for that instance only. This is completely transparent. Same with deletions and newly created files - which will only affect the upper directory currently in use. The user who did the changes will see it in their instance, but it won't affect the lower directory or other peoples' instances.
Over time if different people add different things in to their own instance of it, they'll end up getting more and more different but if you ever want to consolidate things you can periodically go through and determine anything that should be the same for all users and move it into the normally read-only lower directory.
The only issue I can forsee with this setup (which is the same for both solutions) is that if a user wants to share a file with the other users, anything they add won't be shared and will only be visible to them. If you want that, there's another possibility.