By enabling the simultaneous engagement of two distinct targets, bispecific antibodies broaden the potential utility of antibody-based therapies. However, bispecific-antibody design and production remain challenging, owing to the need to incorporate two distinct heavy and light chain pairs while maintaining natural nonimmunogenic antibody architecture. Here we present a bispecific-antibody production strategy that relies on co-culture of two bacterial strains, each expressing a half-antibody. Using this approach, we produce 28 unique bispecific antibodies. A bispecific antibody against the receptor tyrosine kinases MET and EGFR binds both targets monovalently, inhibits their signaling, and suppresses MET and EGFR-driven cell and tumor growth. Our strategy allows rapid generation of bispecific antibodies from any two existing antibodies and yields milligram to gram quantities of bispecific antibodies sufficient for a wide range of discovery and preclinical applications.