Computational protein design of an ensemble of conformations for one protein-i.e., multi-state design-determines the side chain identity by optimizing the energetic contributions of that side chain in each of the backbone conformations. Sampling the resulting large sequence-structure search space limits the number of conformations and the size of proteins in multi-state design algorithms. Here, we demonstrated that the REstrained CONvergence (RECON) algorithm can simultaneously evaluate the sequence of large proteins that undergo substantial conformational changes. Simultaneous optimization of side chain conformations across all conformations increased sequence conservation when compared to single-state designs in all cases. More importantly, the sequence space sampled by RECON MSD resembled the evolutionary sequence space of flexible proteins, particularly when confined to predicting the mutational preferences of limited common ancestral descent, such as in the case of influenza type A hemagglutinin. Additionally, we found that sequence positions which require substantial changes in their local environment across an ensemble of conformations are more likely to be conserved. These increased conservation rates are better captured by RECON MSD over multiple conformations and thus multiple local residue environments during design. To quantify this rewiring of contacts at a certain position in sequence and structure, we introduced a new metric designated 'contact proximity deviation' that enumerates contact map changes. This measure allows mapping of global conformational changes into local side chain proximity adjustments, a property not captured by traditional global similarity metrics such as RMSD or local similarity metrics such as changes in φ and ψ angles.