Thousands of recombinant antibodies enriched for specificity against defined targets are assembled in multivalent mixtures with enhanced therapeutic activity. Plasma-derived polyclonal antibody therapeutics, such as intravenous immunoglobulin, have multiple drawbacks, including low potency, impurities, insufficient supply and batch-to-batch variation. Here we describe a microfluidics and molecular genomics strategy for capturing diverse mammalian antibody repertoires to create recombinant multivalent hyperimmune globulins. Our method generates of diverse mixtures of thousands of recombinant antibodies, enriched for specificity and activity against therapeutic targets. Each hyperimmune globulin product comprised thousands to tens of thousands of antibodies derived from convalescent or vaccinated human donors or from immunized mice. Using this approach, we generated hyperimmune globulins with potent neutralizing activity against severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) in under 3 months, Fc-engineered hyperimmune globulins specific for Zika virus that lacked antibody-dependent enhancement of disease, and hyperimmune globulins specific for lung pathogens present in patients with primary immune deficiency. To address the limitations of rabbit-derived anti-thymocyte globulin, we generated a recombinant human version and demonstrated its efficacy in mice against graft-versus-host disease.