The complexity and relative expressiveness of Ontology-mediated Queries (OMQs) is quite well understood by now. In this paper, we study the expressive power of OMQs from a descriptive complexity perspective, where the central question is to understand whether a given OMQ language is powerful enough to express all queries that can be computed within some bound on time or space. We show that the OMQ language that pairs instance queries with ontologies in the very expressive DL ALCHOI with closed predicates cannot express all coNP-computable Boolean queries, despite being coNP-complete in data complexity. We, then, propose an extension of this OMQ language that is expressive enough to precisely capture the class of all Boolean queries computable in coNP. This involves adding functionality as well as path expressions and nominal schemata, which are restricted in a way that allows us to carefully incorporate them into the existing mosaic technique for the DL ALCHOIF with closed predicates without affecting the coNP upper bound in data complexity.