Full Idea
We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to.
Gist of Idea
We could add axioms to make sets either as small or as large as possible
Source
David Bostock (Philosophy of Mathematics [2009], 6.4)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.188
A Reaction
Bostock says most mathematicians reject the first option, and are undecided about the second option.