Social norms are commonly understood as rules that dictate which behaviors are appropriate, permissible, or obligatory in different situations for members of a given community. Many researchers have sought to explain the ubiquity of social norms in human life in terms of the psychological mechanisms underlying their acquisition, conformity, and enforcement. Existing theories of the psychology of social norms appeal to a variety of constructs, from prediction-error minimization, to reinforcement learning, to shared intentionality, to domain-specific adaptations for norm acquisition. In this paper, we propose a novel methodological and conceptual framework for the cognitive science of social norms that we call normative pluralism. We begin with an analysis of the explanatory aims of the cognitive science of social norms. From this analysis, we derive a recommendation for a reformed conception of its explanandum: a minimally psychological construct that we call normative regularities. Our central empirical proposal is that the psychological underpinnings of social norms are most likely realized by a heterogeneous set of cognitive, motivational, and ecological mechanisms that vary between norms and between individuals, rather than by a single type of process or distinctive norm system. This pluralistic approach, we suggest, offers a methodologically sound point of departure for a fruitful and rigorous science of social norms.