Excellent question. It implies an infinite number of statements. For if T is such an incomplete theory and X is a statement true in some models of T and false in others, then T+X is also a theory that satisfies the same requirements as T in Godel's theorem. Therefore there is another statement Y that is true in some models of T+X and false in other models of T+X. But any model of T+X is a model of T so Y is true in some models of T and false in others. And it goes on...