The SARS-CoV-2 Omicron variant of concern (VoC) and its sublineages contain 31-36 mutations in spike and escape neutralization by most therapeutic antibodies. In a pseudovirus neutralization assay, 66 of the nearly 400 candidate therapeutics in the Coronavirus Immunotherapeutic Consortium (CoVIC) panel neutralize Omicron and multiple Omicron sublineages. Among natural immunoglobulin Gs (IgGs), especially those in the receptor-binding domain (RBD)-2 epitope community, nearly all Omicron neutralizers recognize spike bivalently, with both antigen-binding fragments (Fabs) simultaneously engaging adjacent RBDs on the same spike. Most IgGs that do not neutralize Omicron bind either entirely monovalently or have some (22%-50%) monovalent occupancy. Cleavage of bivalent-binding IgGs to Fabs abolishes neutralization and binding affinity, with disproportionate loss of activity against Omicron pseudovirus and spike. These results suggest that VoC-resistant antibodies overcome mutagenic substitution via avidity. Hence, vaccine strategies targeting future SARS-CoV-2 variants should consider epitope display with spacing and organization identical to trimeric spike.