Which licensing model should I use to share software within a company?

This is just hypothetical at this point. So just doing some ground work to understand, if this is even possible. If yes, which licensing model is most appropriate?

Our company has several units. In many cases, type of technology work done also overlaps. However, each unit does its own thing. So I feel that is there is lot of duplicate work being done.

So I want to propose a common open source model (just within the company), when developing new idea/product, where anyone from any unit can contribute towards the development/enhancement of the product. I am also okay with the product being used by the unit for other purposes within their unit, without any cost. But if they were to make any customization, I want it to be contributed back to main repo. Will I be able to legally enforce this, just internally?

These units also have their own clients that they service. However, I also want to allow these units be able to sell the product based on their billing model (either for services, support or license itself). When they use it at their respective client location, I still want the software to be deemed as proprietary from company perspective.

Now, please suggest, if this is even possible. If yes, what kind of licensing model that would be more appropriate?