In this paper, we analyze a set of systems using different logical combinations of distinct versions of two main ABCD constraint types, CORR and CC.ID. The typologies of these systems are analyzed both extensionally (in terms of the languages predicted) and intensionally (the rankings that produce these languages). The former connects to the empirical predictions generated by the different ABCD theories. The latter connects to the theoretical mechanisms responsible for those predictions, allowing us to compare not just the outputs, but the theories themselves and the reasons for their converging or diverging typological predictions. We show that the same set of extensional languages is produced by all systems in which some correspondence constraint type is restricted, such that failing its precondition allows for vacuous satisfaction. It is not crucial which constraint type bears this restriction, but that it be instantiated in the system as a whole.