I'm writing in second-person just because its easy, for you.
You are working with a game engine and really wish a particular engine class had a new method that does 'bla'. But you'd rather not spread your 'game' code into the 'engine' code.
So you could derive a new class from it with your one new method and put that code in your 'game' source directory, but maybe there's another option?
So this is probably completely illegal in the C++ language, but you thought at first, "perhaps I can add a new method to an existing class via my own header that includes the 'parent' header and some special syntax. This is possible when working with a namespace, for example..."
Assuming you can't declare methods of a class across multiple headers (and you are pretty darn sure you can't), what are the other options that support a clean divide between 'middleware/engine/library' and 'application', you wonder?