Well as WordPress is open source, if you have control of your server, you can technically do anything 🙂 Depending on your skill set, that may or may not be feasible.
A low tech solution would be to create a copy of the theme ABC for each user. Change the folder name, and change the Theme Name in the comment at the top of style.css to personalise it to each user (e.g. “ABC for Bob”, “ABC for Clare”). The codex on child themes is a good starting point for information about this.
I’m not aware of any API calls to detect changes through the theme editor, so I think you’d have to patch the core WordPress install. I had a brief search for where this might be. Using exec() to copy the theme directory would be pretty simple, but the user interaction and updating which version of the theme is being used could make it a bit more complicated.
Of course this is further complicated by the fact that the ‘edit’ function on a multisite is only available to the network admins.