An effective human immunodeficiency virus 1 (HIV-1) vaccine will most likely have to elicit broadly neutralizing antibodies (bNAbs) to overcome the sequence diversity of the envelope glycoprotein (Env). So far, stabilized versions of Env, such as SOSIP trimers, have been able to induce neutralizing antibody (NAb) responses, but those responses are mainly strain-specific. Here we attempted to broaden NAb responses by using a multivalent vaccine and applying a number of design improvements. First, we used highly stabilized SOSIP.v9 trimers. Second, we removed any holes in the glycan shields and optimized glycan occupancy to avoid strain-specific glycan hole responses. Third, we selected five sequences from the same clade (B), as we observed previously that combining Env trimers from clade A, B and C did not improve cross-reactive responses, as they might have been too diverse. Fourth, to improve antibody (Ab) responses, the Env trimers were displayed on two-component I53-50 nanoparticles (NPs). Fifth, to favor activation of cross-reactive B cells, the five Env trimers were co-displayed on mosaic NPs. Sixth, we immunized rabbits four times with long intervals between vaccinations. These efforts led to the induction of cross-reactive B cells and cross-reactive binding Ab responses, but we only sporadically detected cross-neutralizing responses. We conclude that stabilized HIV-1 Env trimers that are not modified specifically for priming naive B cells are unable to elicit strong bNAb responses, and infer that sequential immunization regimens, most likely starting with specific germline-targeting immunogens, will be necessary to overcome Env's defenses against the induction of NAbs. The antigens described here could be excellent boosting immunogens in a sequential immunization regimen, as responses to bNAb epitopes were induced.