It is, perhaps, not the most creative name I’ve ever come up with, but Noram is a holdover term from when the United States formed a coalition bloc with Mexico and Canada to contend with Unified Oceania and the reborn European Union in the early 2100′s. The simply named North American Bloc was abbreviated to NorAm in common speech. Long after the apocalypse, the term stuck around and everyone just assumed that’s what the land was called. Precious few people even know that there’s anywhere else to go.
The default campaign setting is dropped into North America, but nothing stops any aspiring GM from setting the game in Europe, Asia, Africa, or anywhere other than Australia. Do not go to Australia in the characters’ modern day.
“double-edged sword between both you and the other person’s foreheads.“
Purely as an aside, but that’s definitely a bar game played by adventurers with too much booze in their systems. It’s like the knife-between-the-fingers game… Just with your head. And your buddy’s head. And a sword rather than a knife. Okay, it’s completely different, but you take my meaning.
Anyway! Psionics!
Your suggestion is an excellent one, and is already represented when straight up telepathy is involved, but that just scratches the surface of what Mental Mutations can do. To name a few effects, you can…
Light someone on fire, cause hallucinations, hypnotize your foes, see the future, move things with your mind, levitate yourself, teleport, move through solid matter, create a force barrier, make someone berserk with rage, throw lightning bolts, become a walking nuclear reaction, slow down time, alter gravity, or make someone really dizzy.
It’s a bit of a grab bag of capabilities and that’s what made it difficult to create Abilities to work with those effects.

Just substitute cats for powerful psychic abilities and you get the idea.
Sophie’s Choice much?
Nah, it’s not that hard a choice; I’ll take scifi all day, every day, and twice on Fridays. It’s a bit of a cheat answer though, since it could be post-apocalypse, space opera, urban arcana, or if you’re really ballsy, hard SF… Lots of variety and flavor.
Rest of my group isn’t so fond of scifi though, so bleh.
That said, I will always go back to DnD. I’ve been playing since 2nd edition and it’s really become a rather comfortable mental space to drop into. Simpler too! Dragons are color-coded for your convenience, all celestials are good, the door is always trapped, and fighters get a d10 for HP.
Oh, it’s happened before. I’ve seen players attempt everything from the purely mechanical Furiosa Special,

to the more advanced Orky variety with pneumatic pumps and sometimes even electronics!

There are OldTech cybernetic enhancements one can acquire, though those are not only exceedingly rare, but also stupidly complex to install in a living person that isn’t a pure strain human and also wants to survive the procedure. If a group of adventurers are fortunate enough to plunder an ancient medical facility that also still has power, working systems, and maybe a friendly AI to boot, cybernetic augmentation may be possible!
Hooooooo boy… Not asking any easy questions, eh?
Alright, remember how I talked about genetic mutation back here? No? Alright, well, the important bit was how mutant humans had such a jumble of DNA that mutations can readily appear and are often stable. That same variety also allows mutant humans to breed with other species, leading to individuals with the Hybrid Edge.

Hybrid mutants are almost always born to mutant human females with males of other species, but the inverse isn’t impossible… Merely very uncommon. In general, the hybrids tend to appear more human than their male parentage’s species, but some features are bound to bleed through into the offspring: changes to skin or hair, musculature and height, abnormal teeth length, or any other prominent features from the father’s species are likely.
So, if a mutant human, female, player character has a penchant for boinking mutant plants, there is a chance that she’ll end up carrying a baby with green skin and leaves for hair. Do I have rules for it? No. Will I be including a brief entry in the GM’s guide to handle situations when a PC wants to run a character pregnancy? Probably.
If I were cornered by my players who wanted to play out a pregnancy right now, I would probably have some Endurance checks be rolled with minor DCs and then ask them to describe what their characters do during the intervening months/years. From there, child NPCs…
Was going to find a good, meme-y picture to wrap this up, but I also don’t want to do a google search for “half-breed mutant child.” Instead, have some related Krieger.