git - develop base and extended feature - commits in base should reflect in extended in pull
Because you have a large project with multiple teams using multiple development branches will give you merge headaches, especially if the core and extended features have a significant overlap in the codebase. 

The extended feature team(s) will spend a lot of time periodically merging the core feature changes and dealing with the fallout from each such merge, which can not be properly/realistically estimated ahead of time. If there are multiple teams working on the extended feature they might decide to go on separate branches to further isolate and protect themselves against these periodic merge instabilities. It's just an illusion, that'll make things even worse at the overall project level - it can lead to Branch Merge Hell.

You may want to take a look at Trunk-Based Development (TBD), with feature-flags and/or branch by abstraction. Most effective when using a gated-commit CI system.