Organic mind transfer

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Is it possible in theory to transport the mind into a different vessel?
In this case, I'm not referring to anything cybernetic.

With the right technology, obviously you could surgically remove the brain and spinal cord, and place them into an "empty" vessel genetically identical to yourself. However you are still limited to however impressive you're genetics were beforehand.

Similarly, head transplants (surgically replacing the entire head on another body) have reached at least proof of concept stages in monkeys, 50 years ago.
https://en.m.wikipedia.org/wiki/Head_transplant
>The grafted heads were able to function - the eyes tracked moving objects and it could chew and swallow.

But what if you wanted a stronger, taller, body and a more intelligent, efficient, brain?
How would you go about approaching this futuristic challenge?