Computational protein design has found great success in engineering proteins for thermodynamic stability, binding specificity, or enzymatic activity in a 'single state' design (SSD) paradigm. Multi-specificity design (MSD), on the other hand, involves considering the stability of multiple protein states simultaneously. We have developed a novel MSD algorithm, which we refer to as REstrained CONvergence in multi-specificity design (RECON). The algorithm allows each state to adopt its own sequence throughout the design process rather than enforcing a single sequence on all states. Convergence to a single sequence is encouraged through an incrementally increasing convergence restraint for corresponding positions. Compared to MSD algorithms that enforce (constrain) an identical sequence on all states the energy landscape is simplified, which accelerates the search drastically. As a result, RECON can readily be used in simulations with a flexible protein backbone. We have benchmarked RECON on two design tasks. First, we designed antibodies derived from a common germline gene against their diverse targets to assess recovery of the germline, polyspecific sequence. Second, we design "promiscuous", polyspecific proteins against all binding partners and measure recovery of the native sequence. We show that RECON is able to efficiently recover native-like, biologically relevant sequences in this diverse set of protein complexes.