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The accumulation of empirical evidence that has been collected in multiple contexts, places, and times requires a more comprehensive understanding of empirical research than is typically required for interpreting the findings from individual studies. We advance a novel conceptual framework where causal mechanisms are central to characterizing social phenomena that transcend context, place, or time. We distinguish various concepts of external validity, all of which characterize the relationship between the effects produced by mechanisms in different settings. Approaches to evidence accumulation require careful consideration of cross-study features, including theoretical considerations that link constituent studies and measurement considerations about how phenomena are quantifed. Our main theoretical contribution is developing uniting principles that constitute the qualitative and quantitative assumptions that form the basis for a quantitative relationship between constituent studies. We then apply our framework to three approaches to studying general social phenomena: meta-analysis, replication, and extrapolation.