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Structural flexibility in germline gene-encoded antibodies allows promiscuous binding to diverse antigens. The binding affinity and specificity for a particular epitope typically increase as antibody genes acquire somatic mutations in antigen-stimulated B cells. In this work, we investigated whether germline gene-encoded antibodies are optimal for polyspecificity by determining the basis for recognition of diverse antigens by antibodies encoded by three VH gene segments. Panels of somatically mutated antibodies encoded by a common VH gene, but each binding to a different antigen, were computationally redesigned to predict antibodies that could engage multiple antigens at once. The Rosetta multi-state design process predicted antibody sequences for the entire heavy chain variable region, including framework, CDR1, and CDR2 mutations. The predicted sequences matched the germline gene sequences to a remarkable degree, revealing by computational design the residues that are predicted to enable polyspecificity, i.e., binding of many unrelated antigens with a common sequence. The process thereby reverses antibody maturation in silico. In contrast, when designing antibodies to bind a single antigen, a sequence similar to that of the mature antibody sequence was returned, mimicking natural antibody maturation in silico. We demonstrated that the Rosetta computational design algorithm captures important aspects of antibody/antigen recognition. While the hypervariable region CDR3 often mediates much of the specificity of mature antibodies, we identified key positions in the VH gene encoding CDR1, CDR2, and the immunoglobulin framework that are critical contributors for polyspecificity in germline antibodies. Computational design of antibodies capable of binding multiple antigens may allow the rational design of antibodies that retain polyspecificity for diverse epitope binding.