Case studies commonly form the pedagogical backbone in law, ethics, and many other domains that face complex and ambiguous societal questions informed by human values. Similar complexities and ambiguities arise when we consider how AI should be aligned in practice: when faced with vast quantities of diverse (and sometimes conflicting) values from different individuals and communities, with \textit{whose} values is AI to align, and \textit{how} should AI do so? We propose a complementary approach to constitutional AI alignment, grounded in ideas from case-based reasoning (CBR), that focuses on the construction of policies through judgments on a set of cases. We present a process to assemble such a \textit{case repository} by: 1) gathering a set of ``seed'' cases---questions one may ask an AI system---in a particular domain from discussions in online communities, 2) eliciting domain-specific key dimensions for cases through workshops with domain experts, 3) using LLMs to generate variations of cases not seen in the wild, and 4) engaging with the public to judge and improve cases. We then discuss how such a case repository could assist in AI alignment, both through directly acting as precedents to ground acceptable behaviors, and as a medium for individuals and communities to engage in moral reasoning around AI.