I ran a parallel thought experiment that was a little easier, but I think it might shed some light on the harder one you proposed.
I took a radio, tuned it in to a music station, and then began systematically replacing parts. With each change, I made sure that I was still able to hear the music coming out of it. And, you were right. I was able to replace wires with other bits of metal; I replaced the transistors with some old fashioned tubes I still had; I made some capacitors by rolling up tin-foil and waxed paper; etc. (I did this only in my thoughts.)
Now, by removing any change which made the radio fail, and keeping only those that made it work, I suppose you could completely change, say, an analog transistor radio to an old fashioned tube type radio. You might have trouble smoothly transforming a digital radio to an analog one, however.
In this second, easier, experiment, we have the advantage of knowing what is going on in the theory of operation of the radio. And, as long as our new device can detect and amplify the incoming radio signal, building a duplicate but different device is conceptually possible.
My hunch is that the brain is a two-way communication device (more like a cell phone than a radio) connecting our bodies (brains) to the consciousness of ____. I will leave the blank for you to fill. I was going to write 'God', but since my concept of God is probably unacceptable to everyone else, believers and non-believers alike, I had probably better stop using that term.
I used to think of myself as a Theist, since I believe in some kind of thinking transcendent God. But after some more reflection, maybe I am an agnostic instead.
I know! I must be a dyslexic agnostic: I wonder if there really is a Dog.