There are many ways of construing the claim that some categories are more “natural" than others. One can ask whether a system of categories is innate or acquired by learning, whether it pertains to a natural phenomenon or to a social institution, whether it is lexicalized in natural language or requires a compound linguistic expression. This renders suspect any univocal answer to this question in any particular case. Yet another question one can ask, which some authors take to have a bearing on the issue of the naturalness of categories, is whether a system of categories constitutes a unique way of organizing a particular set of entities or phenomena, or whether there are other legitimate classification schemes that can coexist with it. Another way of putting this is by asking whether systems of categories can cut across one another, and if so, under what circumstances. Some philosophers have claimed that crosscutting systems of categories cannot exist as genuine natural kinds. This paper examines that claim and puts forward some counterexamples, concluding that this notion of natural kind is not in tune with scientific classification and ought to be rejected in favor of an alternative.