Specific protein-protein interactions are crucial in signaling networks and for the assembly of multi-protein complexes, and represent a challenging goal for protein design. Optimizing interaction specificity requires both positive design, the stabilization of a desired interaction, and negative design, the destabilization of undesired interactions. Currently, no automated protein-design algorithms use explicit negative design to guide a sequence search. We describe a multi-state framework for engineering specificity that selects sequences maximizing the transfer free energy of a protein from a target conformation to a set of undesired competitor conformations. To test the multi-state framework, we engineered coiled-coil interfaces that direct the formation of either homodimers or heterodimers. The algorithm identified three specificity motifs that have not been observed in naturally occurring coiled coils. In all cases, experimental results confirm the predicted specificities.