I think that only MC will be able to switch.So much we still don't know about Persona 5's mechanics. All PV3 really told us on that front is that you can still acquire new personas.
Hopefully everyone will be customisable this time around, and I wouldn't mind if they just drop the wildcard stuff altogether and just have it so that anyone can switch personas, no story justification needed.
Summoning personas is tied to the masks and only MC's mask is generic looking. Masks of other party members more or less resemble their personas.