There was an experiment I read about some years ago where electrodes were implanted into the brain of a monkey. The electrodes were connected to servos in a stationary robotic arm and after training the monkey was able to feed itself a treat with the robotic arm while its own limbs were bound so as to be immobile. This is the same thing as a swordsman saying his sword "becomes a part" of their arm. New senses can also be added the same way, and there are experiments that prove it. The brain will simply rewire itself to incorporate new connections. It's also completely possible for a person to survive with literally half a brain, the remaining cells rewire and fill out the work (though this is rare). This is also why a blind person has a greater grasp or resolution of sound.
So yes, permitting miracle medical science or crazy cybernetic implants of the future, you COULD have an extra pair of functioning arms under your control.