Crisp-set Qualitative Comparative Analysis, fuzzy-set Qualitative Comparative Analysis (fsQCA), and multi-value Qualitative Comparative Analysis (mvQCA) have emerged as distinct variants of QCA, with the latter still being regarded as a technique of doubtful set-theoretic status. Textbooks on configurational comparative methods have emphasized differences rather than commonalities between these variants. This article has two consecutive objectives, both of which focus on commonalities. First, but secondary in importance, it demonstrates that all set types associated with each variant can be combined within the same analysis by introducing a standardized notational system. By implication, any doubts about the set-theoretic status of mvQCA vis-à-vis its two sister variants are removed. Second, but primary in importance and dependent on the first objective, this article introduces the concept of the multivalent fuzzy set variable. This variable type forms the basis of generalized-set Qualitative Comparative Analysis (gsQCA), an approach that integrates the features peculiar to mvQCA and fsQCA into a single framework while retaining routine truth table construction and minimization procedures. Under the concept of the multivalent fuzzy set variable, all existing QCA variants become special cases of gsQCA.