A bispecific antibody directed against both the tumor-associated antigen (TAA) prostate-specific membrane antigen (PSMA) and the co-stimulatory T-cell-specific surface glycoprotein CD28, with potential immunostimulating and antineoplastic activities. Upon administration of anti-PSMA/CD28 bispecific antibody REGN5678, this bispecific antibody binds to both CD28 on cytotoxic T-lymphocytes (CTLs) and PSMA found on PSMA-expressing tumor cells. This activates and redirects CTLs to PSMA-expressing tumor cells, which may result in the CTL-mediated cell death of PSMA-expressing tumor cells. PSMA is overexpressed on the surface of metastatic and hormone-refractory prostate cancer cells.