The title is v general. There are at least two kind of modifications - one to minimize the change but just change behaviour and the other is really change the program.

I work for a decade as mainframe technical support mostly install fix. And because of these lately when I spent 3 months as a hobby to change the turbo bridge to take external bridge card. I injected code or hacking of the code like jes2 exit and without touching much the host program modify the host program behaviour.

This is very different from my colleagues who are application programmer who can totally change a cics module involving even changing db2 schema.

What is a modification meant in this title … I wonder.

The former. If you intend to hard-fork then Git's model is already fine. If you're soft-forking and want to model your divergence explicitly then Lappverk might be for you.