This is a model theoretic question. I was reading Kremer & Mints's Dynamic topological logic paper, and it mentioned that by a “standard argument”, every consistent formula is a member of some complete consistent theory. (The definitions for complete, consistent, and theory are pretty much the standard ones as defined in any undergrad logic course; they are also defined on the 8th page (page 140).)
If we have a consistent formula, it's already in S4C (which is basically S4 along with some additional axioms; these are given on the same page). Since S4C is closed under modus ponens and by the definition of a theory.
So basically, it comes down to showing that there actually exist complete consistent theories. My question is how one goes about generating such a theory. This is, I think, what they mean when they say “standard argument.” I'm probably not using creative enough search terms, but a quick Google search doesn't turn up anything too useful. Does anyone know where this “standard argument” can be found (or understand it themselves)?