The appeal of highly-configurable software systems lies in their adaptability to users' needs. Search-based Combinatorial Interaction Testing (CIT) techniques have been specifically developed to drive the systematic testing of such highly-configurable systems. In order to apply these, it is paramount to devise a model of parameter configurations which conforms to the software implementation. This is a non-trivial task. Therefore, we extend traditional search-based CIT by devising 4 new testing policies able to check if the model correctly identifies constraints among the various software parameters. Our experiments show that one of our new policies is able to detect faults both in the model and the software implementation that are missed by the standard approaches.