SARS-CoV-2 variants evade current monoclonal antibody therapies. Bispecific antibodies (bsAbs) combine the specificities of two distinct antibodies taking advantage of the avidity and synergy provided by targeting different epitopes. Here we used controlled Fab-arm exchange to produce bsAbs that neutralize SARS-CoV and SARS-CoV-2 variants, including Omicron and its subvariants, by combining potent SARS-CoV-2-specific neutralizing antibodies with broader antibodies that also neutralize SARS-CoV. We demonstrated that the parental antibodies rely on avidity for neutralization using bsAbs containing one irrelevant Fab arm. Using mass photometry to measure the formation of antibody:spike complexes, we determined that bsAbs increase binding stoichiometry compared to corresponding cocktails, without a loss of binding affinity. The heterogeneous binding pattern of bsAbs to spike, observed by negative-stain electron microscopy and mass photometry provided evidence for both intra- and inter-spike crosslinking. This study highlights the utility of cross-neutralizing antibodies for designing bivalent agents to combat circulating and future SARS-like coronaviruses.