The reality which we can know is finite. — Proximate1

How do you demonstrate that?

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So is there an unknowable basis of reality that is beyond knowledge or definition? — Proximate1

If there is "an unknowable basis of reality ...", then wouldn't that fact itself also be "unknowable" ?

It would be unknowable.
I suppose at this juncture we can only muse whether something does exist beyond our ability to reason or not. Does it matter? If you want it to- just like hidden worlds and pixie dust we are free to conceive wherever our minds can go. We only box ourselves in when we think to some arbitrary wall of oblivion and say there's nothing beyond.
Perhaps musing of yet unheard of reality is our purpose.

We demonstrate this by definition of finite itself. Generally the clue is when you have something that 'is this' and 'is not that', the duality inherent to finite existence solidifies something into a knowable state. 'This red apple' is not the 'rock on the front lawn' these are finite things that are readily identifiable.

Reason is limited. The Real exceeds (i.e. encompasses) reasoning. Is there 'beyond the real'? Is it endless? – to reason-limited (i.e. enabled-constrained)-by-the-real this question makes no sense.

Reason is limited- to the three pounds of grey matter we have between our ears. Our thought s are produced by our brain, which is the mechanism of our perceptions and creativity. It's funny how people tend to wall this up like that which lies outside our knowledge needs a fence to separate real from non-real. But there is necessity in defining reality to a point just to negotiate our daily lives and defining reality helps many people to operate in this world.
Is there 'beyond the real'? This is a semantic journey requiring at least some definition of 'real' and then some way of probing into what might be beyond what is real. We have our senses and our sensibility, then derive some order out of the immediate environment to survive. Anything else is frosting on the cake. I like frosting.