The principal aim of this paper is to present a comprehensive theory of coordination of unlikes, i.e., a theory that is capable of dealing with every phenomenon resulting from coordination of unlikes. The proposed theory accounts not just for standard cases of coordination of unlike arguments and coordination of unlike functors but also for cases involving single-conjunct agreement and what will be called each-conjunct agreement. In the course of the argumentation, it is also shown that, even in a language like English, predicate-argument agreement needs to be described in terms of a relational constraint that is not simply an identity requirement.