It depends how you defining the order relation of normal sets with, if it is the set inclusion relation is the order relation and A not a crisp set/ characteristic function then there exists such B, take a point x such that A(x)
Yes, the considered order relation is the set inclusion. So in your example, B(x)=r and B(y)=A(y) if y is different from x. Clearly, A is a proper subset of B and B is normal. Hence A is not a maximal. Am I right?!