Psi having special abilities would be interesting, there are armor weapons that are like spells. Wands that can do stuff, and such.
So maybe just adding more wands would work? Like maybe there could be a wand that can spawn a new auxiliary that doesn't drop a body when it dies or otherwise doesn't show up as dead when it breaks?
Teleportation sounds interesting, but there should be some mechanic to prevent it from being abusive, either a range limit, energy penalty, or having variance in spawn location. Or just high TU cost.
If Psi could be used like a "mind blast" to mentally inflict stun damage, or actual damage based on if a target could resist would be interesting. Like how we have possession and terror, personally I don't really like how you can only use psi in suits. I can understand psi being worthlessly nerfed without required items, but I think psi should be based more with wands. Like the ghost beam being a secondary attack from the ghost knife.
Being able to get a wand to cast invisibility on oneself would be interesting, perhaps the item would be like Halo's Active Camo function based on your psi skill 1 turn per 25 psi?, and require a hypno device per use? An invisibility grenade, or item like mushroom beer that can be used would be fun.