 Von Neumann (who actually formulated a theory of functions, not sets), Gödel, and Bernays developed closely related systems which admit, in addition to the sets found in ZFC, general collections of these sets. (In Hallett 1984, it is argued that the system of von Neumann was the first system in which the Axiom of Replacement was implemented correctly [there were technical problems with Fraenkel’s formulation], so it may actually be the first implementation of ZFC.)