This is a science-fictional idea, but strikingly probable. You are probably aware the brain is split into two halves, joined by a nerve bundle called the corpus callosum. People with severe epilepsy have had the callosum severed, and ended up having two brains in one body. A left brain controlling the right half, and a right brain controlling the left half. The left brain can speak and can lie, the right brain can write with the left hand to communicate. Until experimenters tried to communicate with each half, the people were unaware they were sharing their body with another half-brain. You can read more details if you were unaware.
Anyway, on to the idea. It seems plausible one could apply a temporary anesthetic to the corpus callosum, and temporarily split a person into two brains. Today that might require drastic steps like brain surgery. In the future it's not hard to imagine a specialized drug or highly targetted drug delivery or nanobots to temporarily numb and disable the zone, without too much shutdown of adjacent tissue.
One could even imagine recreational use if it were safe and simple. It would be quite something to learn just what happens when you are split into two and then re-integrated, and how the reformed whole you would remember the two split experiences. Would your left and right half have a conversation? What would they talk about? How long could you persist in this state before it became difficult to reintegrate? How long after the cutoff would you be cogent enough to do all this (one presumes the cutoff might be a bit of a shock.)
Imagine an SF story where one half of the protagonist's brain decides it doesn't want to re-integrate with the other half, and takes steps to assure this...