The number of positions identified with structural realism in philosophical debates about scientific knowledge has grown significantly in the past decade, particularly with respect to the metaphysical or "ontic" approach (OSR). In recent years, several advocates of OSR have proposed a novel understanding of it in order to side-step a serious challenge faced by its original formulation, eliminative OSR. I examine the conceptual basis of the new, non-eliminative view, and conclude that it too faces a serious challenge, resulting in a dilemma for ontic structuralists regarding the ontological status of objects and properties, and the relative "ontological priority" of these entities with respect to the relations in which they stand.