In people with HIV (PWH) on antiretroviral therapy (ART), immune dysfunction persists, including elevated expression of immune checkpoint (IC) proteins on total and HIV-specific T cells. Reversing immune exhaustion is one strategy to enhance the elimination of HIV-infected cells that persist in PWH on ART. We aimed to evaluate whether blocking CTL-associated protein 4 (CTLA-4), programmed cell death protein 1 (PD-1), T cell Ig domain and mucin domain 3 (TIM-3), T cell Ig and ITIM domain (TIGIT) and lymphocyte activation gene-3 (LAG-3) alone or in combination would enhance HIV-specific CD4+ and CD8+ T cell function ex vivo. Intracellular cytokine staining was performed using human PBMCs from PWH on ART (n = 11) and expression of CD107a, IFN-γ, TNF-α, and IL-2 was quantified with HIV peptides and Abs to IC. We found the following: 1) IC blockade enhanced the induction of CD107a and IL-2 but not IFN-γ and TNF-α in response to Gag and Nef peptides; 2) the induction of CD107a and IL-2 was greatest with multiple combinations of two Abs; and 3) Abs to LAG-3, CTLA-4, and TIGIT in combinations showed synergistic induction of IL-2 in HIV-specific CD8+ and CD107a and IL-2 production in HIV-specific CD4+ and CD8+ T cells. These results demonstrate that the combination of Abs to LAG-3, CTLA-4, or TIGIT can increase the frequency of cells expressing CD107a and IL-2 that associated with cytotoxicity and survival of HIV-specific CD4+ and CD8+ T cells in PWH on ART. These combinations should be further explored for an HIV cure.