How can I extend a class in c++ and make whole project use it?

I'm starting with a project that consist in the "merge" of two functional software.

Software 1 has a class which is instantiated a lot of times (thousands or even millions of times) and uses another class. Now I want to change the behavior of that two classes, to work with Software 2.

I have in mind to create an adapter class so the two programs can communicate, and for the classes, I would like to extend those two classes, but without modifying the code of of the software 1.

The final goal is to have the functional merged software with the external software without coupling and that can be upgraded with future versions without any problem (apart from changing the extended classes and the adapter).

Is this a good/feasible approach? I don't know for what should I start looking. Any opinion or approach is welcome.