The ZX-Calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. The completeness of the π 4-fragment is a main open problem in categorical quantum mechanics, a program initiated by Abramsky and Coecke. It has recently been proven that this fragment, also called Clifford+T quantum mechanics, was not complete, and hence a new rule called supplementarity was introduced to palliate it. The completeness of the π 4-fragment is a crucial question, for it is the " easiest " approximately universal fragment, whereas the π 2-fragment, the stabiliser quantum mechanics, is known to be complete but is not approximately universal. In this paper, we will show that, on the one hand, the π 4-fragment is still not complete despite the new supplementarity rule, and that, on the other hand, this supplementarity rule can be generalised to any natural number n. To prove the incompleteness of the π 4-fragment, we can show an equality over scalars that is not derivable from the set of axioms, and that will lead to a substitute for the inverse rule, and the obsolescence of the zero rule. We can also show that the generalised supplementarity for any n not a power of 2 is not derivable from the current set of axioms of the ZX-Calculus, but that the rule for some n can be derived from some others. The hierarchy of these rules will be discussed.