In recent years, there has been increasing interest in the combination of two methods on the basis of set theory. In our introduction and this special issue, we focus on two variants of cross-case set-theoretic methods - Qualitative Comparative Analysis (QCA) and typological theory – and their combination with process tracing. Our goal is to broaden and deepen set-theoretic empirical research and equip scholars with guidance on how to implement it in multi-method research (MMR). At first

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... set-theoretic cross-case methods and process tracing seem to be highly compatible when causal relationships are conceptualized in terms of set-theory. However, multiple issues have not so far been thoroughly addressed. Our paper builds on the emerging MMR literature and seeks to enhance it in four ways. First, we offer a comprehensive and coherent elaboration of the two sequences in which case studies can be combined with a cross-case method. Second, we expand the perspective and discuss QCA and typological theory as two alternative methods for the cross-case analysis. Third, based on the idea of analytical priority, we introduce the distinction between a condition-centered and a mechanism-centered variant of set-theoretic MMR. Fourth, we point attention to the challenges of theorizing and analyzing arrangements of conditions and mechanisms associated with sufficient conjunctions.