You just blew my mind (no pun intended).
In this thread, we're basically alluding to the Hard Problem of Consciousness[0]. Consciousness is hard to define, and even harder to prove, and so conversations that talk about it become difficult.
There's certainly a certain subset of the brain you can take out and still have no effect on consciousness. Assuming you could replace small parts at a time, what would happen? At what point does the "mind", "self", or "consciousness" get lost?
[0] https://en.wikipedia.org/wiki/Hard_problem_of_consciousness