I kind of liked one of the HPMOR recursive fanfics which played with this since in the Methodsverse wizards continued to be able to think even when their brain was replaced with that of a cat.
If I remember right in that fic the blood-purists maintained that only wizards had souls and that the thing they used to prove it was by feeding polyjuice to a non-wizard who would lose their own personality in favor of the body they were copying for the duration of the potions effects. (not having a magical soul with which to maintain their thought patterns when their physical brain was changed)
No plot spoilers here, just wanted to flag a bit of poor reasoning that shows up in Chapter 39:
This is a surprisingly common fallacy. Just because X depends on Y, it doesn't follow that X depends on nothing but Y. A phenomenon may involve more than just its most obvious failure point.
To illustrate: Suppose I'm trapped in a box, and my only way to communicate with the outside world is via radio communication. Someone on the other end argues that I don't really exist -- "There's no person beyond the radio receiver, for if there was then there wouldn't be any such thing as damaged radios!" Pretty silly, huh? But people say this kind of thing in defense of physicalism all the time.
(N.B. This is not to defend the existence of souls. It's just to point out that this particular argument against them is invalid.)