a set of charts satisfying those requirements that you alluded to is called maximal if any other set of charts which satisfies the conditions is a subset of this one.
i find it a little more comfortable to call any set of charts that satisfies the conditions an atlas. then the above sentence is a little easier to read:
an atlas is maximal if any other atlas on the space is a subset.
by Zorn's Lemma, any space with an atlas has a maximal atlas.