The emergence of SARS-CoV-2 variants of concern underscores the need for antibody-based tools that target multiple sites of the spike protein. We isolated 216 monoclonal antibodies and designed several bispecific antibodies that potently neutralize authentic SARS-CoV-2. Notably, two of nine bispecific antibodies neutralized the Alpha, Beta, Gamma and Delta variants and the wild-type virus with comparable potency. Thus, bispecific antibodies represent a promising next-generation countermeasure against SARS-CoV-2 variants of concern.