In conceptual blending, the transfer of properties from the input spaces relies on a shared semantic base. At the same time, interesting blends are supposed to resolve deep semantic clashes where many concept combinations correspond to impossible blends, i.e. blends whose input spaces lack any obvious similarities. Instead of a shared structure, the blends are based on bidirectional affordance structures. While humans can easily map this information, computational systems for creative constructions require an understanding of how these features relate to one another. In this paper, we discuss this problem from the perspective of linguistics and computational blending and propose a method combining theory weakening and semantic prioritisation. To demonstrate the problem space, we look at the Sesame Street character ‘The Cookie Monster’ and formalise the blending process using description logic.