Safely Change Network enabled theme .php files

We are running a network of sites basing them off a large amount of themes, which we then customize per client.

There is a “Custom CSS” Plugin that lets us override the “style.css” for each one, so we can have
Theme A – (all red stuff) – for client one, and
Theme A – (all blue stuff)- for client two.

This is great! So we don’t need to change any actual files regarding Theme A!

HOWEVER, I need to know if there is a way to edit .PHP files as well, without changing them for EVERY instance of Theme A.

If I want Theme A for clients one and two, is there a way to get them each a separate (or override, like custom CSS) “Featured.PHP” or any php file for that matter?