Science

monkeys with a 3rd robot arm

Not sure if it's the same, but I see a video of that and the monkey's arms are partially restricted and still moving (and another where it says reenactment at the start). Interesting, but it might just be a cloned signal rather than independent control.

Though I guess swapping between sets and some basic controls (hold, gimbal, return to rest pose etc) wouldn't be bad (especially the more naturally it can be controlled) it just seems like something different if it isn't independent control.

full-brain mesh of electrodes, could allow people to use multiple full bodies at once
or that multiple brains couldn’t be connected and made work in parallel (brain hemispheres already do that

I've had the exact opposite thought, multiple brains (in the sense of multiple people) residing in the same body. Usage shifts (to allow rest), partial control, or even simply observation/eyes-in-the-back-of-your-head/backup/advice/talking etc.

That definitely would allow at least 4 arms.

On a sidenote, in the Blender Open Movie CHARGE there's a cool robot design where it starts out with 1 big (no-hand) arm and 2 little arms on the other side and then it transforms that into 2 normal arms.