THis is a r/askscience type of question.
So is there a limit to how many connections your brain can make in terms of controlling your voluntary physical body?
Like would it be impossible to control an extra limb attached to your body even if it had nerves?
Or like would it be impossible to ever learn how to use all your toes as good as fingers because your brain can’t handle that many connections? Or is it even possible to ever learn how to move all toes independently the way you can move your fingers?
Or maybe if your body had extra nerves somewhere you still wouldn’t feel them because your brain already has its connections maxed out.
You know, sort of like a computer where all the usb ports are already used up.
There is some flexibility but hard limits on it. Basically during embryonic development your brain wired up all the I/o it actually found. Muscles chemically request nerves for control to wire to them, sensory patches in your skin and organs ask for sensation nerves, and the nerve cells follow these chemical gradients and plug themselves in. So the easiest way to control another limb is if you are missing your original one.
Now, there is flexibility and with retraining, if someone wired in a brain implant you could learn to somewhat control the connected device. But it would never be as good as your control over the original hardware, unless that implant were basically taking over the I/o for one of your limbs. Then you could control the robotic limb pretty well, but only while leaving the limb those nerves went to limp.
People with no arms, especially if born that way, learn to control their toes pretty well. I imagine the limits to that are in the toes, not the brain, but I don’t know for sure. And I recently heard on quirks and quarks about how people born blind can learn to echolocate, clicking their tongue against the roof of the mouth. It was quite impressive.
I have seen a woman with no arms crochet, and she was damn good at it. I personally can pick things up with my toes. It is clumsy but effective.
Just controlling the limbs I actually have often taxes my ability to and beyond the limit. Says the guy who types with two fingers. 
(I can rub and pat my chest simultaneously with both hands; but, curiously, only when I rub with the right and pat with the left!)