In Combinatory Categorial Grammar (CCG) [Ste90, Ste91], semantic function-argument structures are compositionally produced through the course of a derivation. These structures identify, interalia, which entities play the same roles in different events for expressions involving a wide range of coordinate constructs. This sameness of role (i.e., thematic) information is not identified, however, across cases of verbal diathesis. To handle these cases as well, the present paper demonstrates how to adapt the solution developed in Conceptual Semantics [Jac90, Jac91] to fit the CCG paradigm. The essence of the approach is to redefine the Linking Theory component of Conceptual Semantics in terms of CCG categories, so that derivations yield conceptual structures representing the desired thematic information; in this way no changes are required on the CCG side. While this redefinition is largely straightforward, an interesting problem arises in the case of Conceptual Semantics' Incorporated Argument Adjuncts. In examining these, the paper shows that they cannot be treated as adjuncts in the CCG sense without introducing new machinery, nor without compromising the independence of the two theories. For this reason, the paper instead adopts the more traditional approach of treating them as oblique arguments.