The proper analogy for a Python object is `std::shared_ptr<Foo>`: in Python, all "objects" are actually reference-counted pointers to objects (thus making them shareable). And then yes, in C++, you can change to which object the caller's "object" (pointer-to-object) points to, if you pass a reference to that. This is not possible in Python: all you can do is pass that shared-pointer value around, not the value of the object itself, nor a reference to the shared pointer.

This is a well-known distinction that goes by several names, see e.g. https://en.m.wikipedia.org/wiki/Evaluation_strategy#Call_by_...