Omniscience: A thought experiment

[Mudhammam]

I'd argue that no being CAN be omniscient, because it cannot know whether it is part of a bigger whole-- for example a collection of multiple beings, isolated from each other, who each think they are omniscient.

Why couldn't an omniscient being know that? Your example just assumes that the isolated beings aren't actually omniscient but it doesn't establish the impossibility of omniscience in principle. Presumably an actually omniscient being would know the whole as it knows itself and itself it knows as the whole, and of which it actually is both the knowable and known whole.

It seems to me that you're essentially asking, "Could it know that it knows what it knows?" You can drag that out ad infinitum. The simple answer is yes, if it knows anything, an omniscient being knows that it knows what it knows and what it knows is everything there is to know!