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As far as I understand, Buddhism (Tibetan Gelug is what I am most familiar with) holds that a mindstream is always individual.
Is there any reason against the notion that one mindstream can separate into two (or that mindstreams can merge) ?
Just like a river can separate into two, or many streams can merge into an ocean.
For mind-streams to merge the two must exist in a shared space or a world, like two cars in a garage.
However external minds that can be grasped with wrong view to be personal for another is something conceived of internally by mind which is internal and can be grasped wrong view to be personal for one to whom it is internal & self-referable.
There is no space or world outside of the world conceived & perceived by this or that mind.
In the pali discourses, that in the world through which one conceives & perceives the world is called a world. There is no world to speak of outside of a subjective frame of reference and therefore two frames of reference can not merge.
For another person's frame of reference to merge with the frame of reference which can know it with intellect, that frame of reference of another, of which one thinks about internally as 'percipience which is external', would have to exit the world wherein it is an object of perception and be a world disconnected from the world where it was a truth altogether, before imposing itself as to make perception of the world as we know it absolete.
Two observers do not perceive the same simultaneity of events. A person moving towards light will perceive visible form before one moving away from it, visible light here & there isn't seen simultaneously as those aren't even the same particles.
Check this video on Special Relativity
https://www.youtube.com/watch?v=wteiuxyqtoM&ab_channel=MyEarbot
Therefore if two mind-streams merged that resultant mindstream would contradict itself on account of simultaneity. It would have two pasts and be disconnected from both, eg one past where things were seen to occur consequently and another past where the same events are perceived to occur in a different succession which makes them essentially different events.
In Buddhism, the preoccupation with views of "self" is considered unskillful. Instead of "mindstreams", the Buddha gently points at skillful and unskillful behaviors, showing the path and outcome of each. Unskillful behaviors lead to suffering. However, skillful behaviors lead to the end of suffering. And in this regard of streams of behavior, one hears this about skillful behavior:
AN10.61:4.1: It’s like when the rain pours down on a mountain top, and the water flows downhill to fill the hollows, crevices, and creeks. As they become full, they fill up the pools. The pools fill up the lakes, the lakes fill up the streams, and the streams fill up the rivers. And as the rivers become full, they fill up the ocean.
Reality works in the way of moments of experience. One moment arises and passes away whereafter another moment arises and passes away. That process repeats itself until one is fully liberated from Samsara.
The above process can be seen for oneself through insight meditation practice.
things like oceans and waves are just water function given different names and concepts. this is different to actually differently functioning objects that function that way regardless of what you call them. furthermore each different thing consists of unique collections of parts and if these are removed the functioning object is destroyed
so in your example of the mindstream assuming you could remove a portion of it to attempt to create another it would be destroyed having lost its parts and the capacity to function
you should look into the other indian tibetan buddhist lineages you will appreciate what they have to say...berzin had an awesome article on it. essentially they accept only atoms as real ie. functioning any notion of collections is purely conceptual. further yet the sakyas accept atoms and subtle collections of them as functioning, wholes being entirely conceptual. it is only with tsongkhapa that we finally assert also wholes as being functional and not merely conceptual, since he was the first to explicitly explain emptiness conceptually and emptiness has no problem establishing actual wholes as functioning things while still maintaining that they are mere imputation. it doesn't really matter which system you use even sautrantika level of imputation if you break through and realize its meaning it propels you toward nothing lacking the absence of an essential nature.
