Does there exist a complete classification of all Post complete extensions of the basic conditional logic system CK, analogous to the classical Post completeness theorem for propositional logic?

A complete Post-style classification would provide a definitive map of the expressive boundaries of conditional logic, telling us exactly which collections of conditional principles are internally consistent and maximal. This would have direct consequences for formal epistemology, AI reasoning systems that use counterfactual conditionals, and the foundations of causal inference, where conditional logics are increasingly used to model interventions. It would also illuminate the doctrinal completeness results being developed via categorical logic and type space functors, since understanding maximal theories is prerequisite to understanding the full functor between syntactic and semantic categories in the conditional setting.