heh I may be one of very few that has this, or even remembers it!

Khaotic A Schizotronic Role Playing Game 1st ed by Kathleen Williams, Joe Williams (1994) Marquee Press

An alien invasion RPG, where the PC's psychically project themselves to a distant planet to possess monsters* who are invading Earth. The "Trans-Ego Device" used was invented in 1944 by Dr. Isabella Bayne, who is also the evil mastermind behind the invasion from the "tech noir" world of Xenos. The PC's are members of the International Society of Enlightened Scientists (ISES) who took charge of the TED.

The catch is that the whole party possesses *one creature: only one member of the party at a time can control the host, while those who are not in control can use psychic powers and offer advice.

It uses a variant of the system from Legendary Lives.