To date, immunization studies of rabbits with the BG505 SOSIP.664 HIV envelope glycoprotein trimers have revealed the 241/289 glycan hole as the dominant neutralizing antibody epitope. Here, we isolated monoclonal antibodies from a rabbit that did not exhibit glycan hole-dependent autologous serum neutralization. The antibodies did not compete with a previously isolated glycan hole-specific antibody but did compete with N332 glycan supersite broadly neutralizing antibodies. A high resolution cryoEM structure of one of the antibodies in complex with the BG505 SOSIP.664 trimer demonstrated that, while the epitope recognized overlapped with the N332 glycan supersite by contacting the GDIR motif at the base of V3, the primary contacts were located in the variable V1 loop. These data suggest that strain-specific responses to V1 may interfere with broadly neutralizing responses to the N332 glycan supersite and vaccine immunogens may require engineering to minimize these off-target responses or steer them toward a more desirable pathway.