This is more of "it depends" situation. You could have a part of it change appearance, but it shouldn't be used as a way to get an extra power out of the Persona (so being able to look like other Personas or pretending to be a part of the environment, for example.)

The best suggestions we have for you here would be either to give him ever-changing colors, or clothing on top of his typical form that change every summon, but would still be easily identifiable as your character's persona from a glance.