A set-based approach is presented for exploring multilevel design problems. The approach is applied to design negative stiffness metamaterials with mechanical stiffness and loss properties that surpass those of conventional composites. Negative stiffness metamaterials derive their properties from their internal structure, specifically by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design involves managing complex interdependencies among design variables across a range of length scales. Hierarchical material models are created for length scales ranging from the structure of the microscale negative stiffness inclusions to the effective properties of mesoscale metamaterials to the performance of an illustrative macroscale component. Bayesian network classifiers (BNCs) are used to map promising regions of the design space at each hierarchical modeling level, and the maps are intersected to identify sets of multilevel solutions that are likely to provide desirable system performance. The approach is particularly appropriate for highly efficient, top-down, performance-driven, multilevel design, as opposed to bottom-up, trial-and-error multilevel modeling.