Uh, well, yeah. But, of course, the collective force of the society and culture within any given human culture shapes the definition of normal as well as individual behavior. (See my posts:33,37,39,40)
And there is this long-standing "notion of perfectibility" which has been introduced by Judeao-Christian religions which has systematized certain ideals to which humankind strives. And, finally, there's the notion of a duality: Animal-Man, or Beast-Noble, or Mind-Body (whatever you call it) that has also characterized mankind since...well, forever.
Is there an ultimate definition of "normalcy" and, if so, what is it?
Some people presume there is, others disagree...and on it goes.
Ultimate normalcy is less interesting to me than ultimate purpose. The perfection of a thing is when it fulfills the purpose for which it is made. And to find out what that purpose is, well, you have to consult the Person that made us.
And I think you are not quite understanding "perfectibility" in a Judeo-Christian sense. Perfection in Christianity comes about not through one's own actions/thoughts/powers but as a free gift of grace.
This idea that humanity is approaching perfection apart from grace is the doctrine of secular humanists, socialists, and utopians.