The situation:
I have a basic app with some central functionality.
My clients (potentially many dozens) all want their own customized apps in the app store.
The problem
If I have dozens of apps in the app store and I want to change some of the core functionality, I would have to update each file in the corresponding project, compile, go through iTunes Connect, upload etc. Every small change could potentially take days of mindless work.
The question
Is there a way I can use a versioning system like git to administer the parts of my code with the core functionality separately, so that all projects are updated automatically when I commit a change to the core files?
Is there any other way to make this process easier to manage?