Broadly neutralizing antibodies (bnAbs) targeting the trimer apex of HIV envelope are favored candidates for vaccine design and immunotherapy because of their great neutralization breadth and potency. However, methods of isolating bnAbs against this site have been limited by the quaternary nature of the epitope region. Here we report the use of a recombinant HIV envelope trimer, BG505 SOSIP.664 gp140, as an affinity reagent to isolate quaternary-dependent bnAbs from the peripheral blood mononuclear cells of a chronically infected donor. The newly isolated bnAbs, named "PGDM1400-1412," show a wide range of neutralization breadth and potency. One of these variants, PGDM1400, is exceptionally broad and potent with cross-clade neutralization coverage of 83% at a median IC50 of 0.003 µg/mL. Overall, our results highlight the utility of BG505 SOSIP.664 gp140 as a tool for the isolation of quaternary-dependent antibodies and reveal a mosaic of antibody responses against the trimer apex within a clonal family.