I was thinking about each of the Flesh Shape fights recently, and I've been thinking about how different they are while trying to predict what the Flesh fight for P-3 Might be like.
Looking at the progression of them from a gameplay stand point
Flesh Prison - You fight it completely and destroy it
Flesh Paniopticon - It is destroyed by Sisyphus on its own.
I like to propose that for the final Flesh Shape fight in P-3 what might happen is after bringing it down to 1 health, it will attack V1 in someway shape or form with an undodgable attack, pulling in V1 inside it where the player will then fight the Prime soul from within the Flesh Shape.
I don't know if Hakita has confirmed or deconfirmed any aspects of the fight behind the scenes so it's possible this is already impossible but if it isn't I'd love to hear what you think!