UNIVERSALS
It's one of the oldest debates in philosophy: what makes two things the same kind of a thing? Is it some third thing they both partake in? Is it a component of them? Is it that they aren't really the same kind of thing, but it's just convenient for us to say they are? It is a notoriously difficult question to even explain and you'd be surprised at the potential implications!
Infinity
What is infinity? Is it a number or just a concept? Does it even exist? If it doesn't exist, then how do we seem to have unlimited numbers? If it does exist, then what is the number before it?
PHILOSOPHY of MIND
Do I have a mind that is distinct from my brain? If not, what explains thoughts and experiences? If so, how can it be related to the body?
Metametaphysics
What exactly are we doing when we do metaphysics? Are we talking about real things? What justifies metaphysical conclusions?
PHILOSOPHY of NATURE
What is the nature of things?