This invention provides new compositions comprising nucleotide sequence(s) encoding alphaherpesvirus glycoprotein D protein(s) (gDP(s)) and antigen(s) that induce immune responses. Such sequences typically encode gDP:antigen fusion proteins and typically also include feature(s) that significantly enhance immune responses such as (a) sequences encoding ITIC signal transducing adaptor proteins, e.g., SLAM-associated proteins (SAPs), Ewing's sarcoma-associated transcript 2 proteins, or both, or non-gDP checkpoint inhibitor(s); (b) sequences encoding antigen-associated targeting sequences, e.g., polyubiquitin sequences; (c) deimmunized/modified antigen-encoding sequences; (d) gDP(s) with modified sequence(s); (e) expression-enhancing introns; (f) transfection-facilitating agents; or (g) combinations thereof. Methods of using such constructs to induce immune responses and other methods and compositions also are provided, including methods of using such constructs in animals not known to express Herpesvirus entry mediator (HVEM) receptors (e.g., pigs), animals not under disease agent-associated checkpoint inhibition, and other contexts.