In many languages with clitic or other weak pronouns, a Person-Case Constraint (Perlmutter 1971, Bonet 1991) prohibits certain combinations of these pronouns on the basis of their person features. This article explores the crosslinguistic variation in such constraints, starting with several closely related Zapotec varieties. These restrict combinations of clitics not just on the basis of person, but also on the basis of a finely articulated, largely animacy-based gender system. Operating within a larger combinatorial space, these constraints offer a new perspective on the typology of Phi-Case Constraints (ΦCCs) more generally. This typology has an overall asymmetrical shape correlating with the underlying syntactic position of pronominal arguments. We develop a principled theory of this typology that incorporates three hypotheses: (a) ΦCCs arise from how a functional head Agrees with clitic pronouns, subject to intervention-based locality (Anagnostopoulou 2003, Béjar and Rezac 2003, 2009); (b) the variation in these constraints arises from variation in the relativization of probes (Anagnostopoulou 2005, Nevins 2007, 2011); and (c) clitic and other weak pronouns have no inherent need to be licensed via Agree with a functional head. Under this account, the crosslinguistic typology of ΦCCs has the potential to shed light on the grammatical representation of person and gender.