The receptor-binding domain (RBD) of influenza virus hemagglutinin (HA) elicits potently neutralizing yet mostly strain-specific antibodies. Here, we evaluate the ability of several immunofocusing techniques to enhance the functional breadth of vaccine-elicited immune responses against the HA RBD. We present a series of "trihead" nanoparticle immunogens that display native-like closed trimeric RBDs from the HAs of several H1N1 influenza viruses. The series includes hyperglycosylated and hypervariable variants that incorporate natural and designed sequence diversity at key positions in the receptor-binding site periphery. Nanoparticle immunogens displaying triheads or hyperglycosylated triheads elicit higher hemagglutination inhibition (HAI) and neutralizing activity than the corresponding immunogens lacking either trimer-stabilizing mutations or hyperglycosylation. By contrast, mosaic nanoparticle display and antigen hypervariation do not significantly alter the magnitude or breadth of vaccine-elicited antibodies. Our results yield important insights into antibody responses against the RBD and the ability of several structure-based immunofocusing techniques to influence vaccine-elicited antibody responses.