Neutralizing monoclonal antibodies have achieved great efficacy and safety for the treatment of numerous infectious diseases. However, their neutralization potency is often rapidly lost when the target antigen mutates. Instead of isolating new antibodies each time a pathogen variant arises, it can be attractive to adapt existing antibodies, making them active against the new variant. Potential benefits of this approach include reduced development time, cost, and regulatory burden. Here a methodology is described to rapidly evolve neutralizing antibodies of proven activity, improving their function against new pathogen variants without losing efficacy against previous ones. The reported procedure is based on structure-guided affinity maturation using combinatorial mutagenesis and phage display technology. Its use against the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is demonstrated, but it is suitable for any other pathogen. As proof of concept, the method is applied to CoV-X2, a human bispecific antibody that binds with high affinity to the early SARS-CoV-2 variants but lost neutralization potency against Delta. Antibodies emerging from the affinity maturation selection exhibit significantly improved neutralization potency against Delta and no loss of efficacy against the other viral sequences tested. These results illustrate the potential application of structure-guided affinity maturation in facilitating the rapid adaptation of neutralizing antibodies to pathogen variants.