This versatile advantage can occur as part of many powers. The most obvious of these are supernatural; for example, a divine power that lets a priest take on the forms associated with his god, or a spirit power that enables a shaman to become a totem animal. A dimension travel power might give the wielder the ability to appear in different bodies, storing unused ones “elsewhere” for the duration. And a body-control power could give the user enough control that he can turn into something else.
GURPS Horror 72 has the example of the Wendigo, where when a Spirit is possessing someone, they are able to use their Alternate Form to alter the possessed body.
The same applies to the ST bonus.
Neither are given any kind of cosmic modifier, only limitations.
The Affliction also doesn't really make any kind of sense, because mental disadvantages of the host body are overridden by the mental traits of the possessor.
I agree with the attacker taking 10 seconds of Concentration for the Affliction (Alternate Form)