The antigen-binding fragment of the broadly neutralizing human immunodeficiency virus type 1 (HIV-1) antibody 2G12 has an unusual three-dimensional (3D) domain-swapped structure with two aligned combining sites that facilitates recognition of its carbohydrate epitope on gp120. When expressed as an intact immunoglobulin G (IgG), 2G12 formed typical IgG monomers containing two combining sites and a small fraction of a higher-molecular-weight species, which showed a significant increase in neutralization potency (50- to 80-fold compared to 2G12 monomer) across a range of clade A and B strains of HIV-1. Here we show that the higher-molecular-weight species corresponds to a 2G12 dimer containing four combining sites and present a model for how intermolecular 3D domain swapping could create a 2G12 dimer. Based on the structural model for a 3D domain-swapped 2G12 dimer, we designed and tested a series of 2G12 mutants predicted to increase the ratio of 2G12 dimer to monomer. We report a mutation that effectively increases the 2G12 dimer/monomer ratio without decreasing the expression yield. Increasing the proportion of 2G12 dimer compared to monomer could lead to a more potent reagent for gene therapy or passive immunization.