Daily burden and clinical toxicities associated with antiretroviral therapy (ART) emphasize the need for alternative strategies to induce long-term human immunodeficiency virus (HIV) remission upon ART cessation. Broadly neutralizing antibodies (bNAbs) can both neutralize free virions and mediate effector functions against infected cells and therefore represent a leading immunotherapeutic approach. To increase potency and breadth, as well as to limit the development of resistant virus strains, it is likely that bNAbs will need to be administered in combination. It is therefore critical to identify bNAb combinations that can achieve robust polyfunctional antiviral activity against a high number of HIV strains. In this study, we systematically assessed the abilities of single bNAbs and triple bNAb combinations to mediate robust polyfunctional antiviral activity against a large panel of cross-clade simian-human immunodeficiency viruses (SHIVs), which are commonly used as tools for validation of therapeutic strategies targeting the HIV envelope in nonhuman primate models. We demonstrate that most bNAbs are capable of mediating both neutralizing and nonneutralizing effector functions against cross-clade SHIVs, although the susceptibility to V3 glycan-specific bNAbs is highly strain dependent. Moreover, we observe a strong correlation between the neutralization potencies and nonneutralizing effector functions of bNAbs against the transmitted/founder SHIV CH505. Finally, we identify several triple bNAb combinations comprising of CD4 binding site-, V2-glycan-, and gp120-gp41 interface-targeting bNAbs that are capable of mediating synergistic polyfunctional antiviral activities against multiple clade A, B, C, and D SHIVs. Optimal bNAb immunotherapeutics will need to mediate multiple antiviral functions against a broad range of HIV strains. Our systematic assessment of triple bNAb combinations against SHIVs will identify bNAbs with synergistic, polyfunctional antiviral activity that will inform the selection of candidate bNAbs for optimal combination designs. The identified combinations can be validated in future passive immunization studies using the SHIV challenge model.