I'm assuming that your hypothetical Antagonist is also the Influence Character (IC), right? Because the Antagonist on its own does not have a personal "arc" -- it has the same prob/sol/sym/resp as the Overall Story Throughline because it is merely a fragment of that throughline.
The MC and IC never have identical throughline elements. The cross-throughline congruencies are typically:
Problem & Solution: Change MC or IC matches OS. (Also matches RS if Judgment = Bad)
Symptom & Response: Steadfast MC or IC matches OS. (Also matches RS if Judgment = Good)
Tinker around with the software and you'll see how the cards fall.
I know it is a popular notion to have the villain 'mirror' the hero. Pixar artists say as much in The Art of UP: they intended Muntz to be a forewarning to Karl, as in, "this is the kind of crazy old man you could become if you don't change your ways!"
I think this idea just sort of emerged out of an unconscious recognition for something like an Influence Character in stories, but latched onto the "Villain" because that's the popular lingo. Even if there is a consistent IC in UP, it's certainly not Muntz, and so this bit of storyweaving doesn't really feel impactful.