Not happening. The Twenty-second Amendment was an anti-communist reaction by the terrified bourgeoise and their political puppets to officially curtail the power of the presidency after the realization that if such a powerful office fell into the hands of anyone with even a hint of social democratic tendency - or worse - their dominance upon the political sphere could easily be unraveled by the stroke of a pen.
Of course one can posit "what if the president and their administration really didn't care about 'rules and norms' and simply wielded power as they truly saw fit", that I would say, is where the MegaCoolZone would really kick off.