Omniscience: A thought experiment

[bennyboy]

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!

lol
We didn't stipulate that it knows everything THERE IS to know.  We stipulated that it knows everything-- including whether what it knows is everything there is to know.
But I cannot conceive of an entity, no matter how great, that can know for sure that there is nothing that might not be known to it.

Let's say you're God-- how do you know there is no other God? Haven't experienced one? Never met one?