It was once believed by scientists that split-brain people, those that had had their corpus callosum severed, developed different personalities in the two halves. But when the experiments were replicated decades later, it turned out that the two halves of the brain, despite only having 1% of the ability to communicate between the halves as before, still managed to present one persona. It’s still unclear as to why this is the case.
I believe you are mistaking terms here. What you are calling mind, other people would call consciousness. What you are calling consciousness, other people would call mind. Consciousness is the mechanism by which beings experience things. By your phrasing, you want to know whether you can have two different “experience functions”, producing one mind.
Consciousness is experience, so what is mind? Mind is thought. Many thoughts contribute to one experience. When you remember something, you’re replicating an experience. If you meditate on this, experience and thoughts are quite different things. Experience includes thought, not the other way around.
So the idea that you can have multiple consciousnesses living in a brain is a bit silly. Fodder for science fiction or horror movies, but nothing that actually happens. Multiple personality disorder works by splitting consciousness up among different minds, not by splitting the mind up among multiple consciousnesses.