You can read studies of people who had their corpus callosum severed. This cuts off all communication between left and right hemispheres permanently. They maintain full and normal function, but the left and right halves of their bodies seem to take on independent lives mostly unaware of each other. You can ask a question and the mouth will give one answer but the left hand may write out a completely different answer (vocal language processing is controlled by the left hemisphere, where left arm is controlled by the right hemisphere).

This suggests even just half the brain can maintain the full set of higher cognitive abilities of a normal healthy human, but only half the motor control, which is presumably more dependent on hard-coded IO ports between the brain itself and the nerve buses running to the actual body part being controlled.

Which is to say there is an actual "right side of the face" zone, but there is no zone for higher reasoning in general. Unless you destroy the entire frontal cortex, much smaller subsets of it can fully function as if whole.

I think Daniel Dennett used this evidence to argue that the entire notion of self is an illusion. The brain is so highly redundant that it really consists of countless selves, a distributed system that dynamically comes to consensus but each component is fully capable of operating on its own or as part of a smaller distributed system when the network gets partitioned.