This study is an open-label, Phase 1, multicenter study to evaluate the safety, tolerability, pharmacokinetics (PK), and pharmacodynamic (PD) profiles of a novel fragment crystallizable (Fc)-engineered immunoglobulin G1 anti-cytotoxic T-lymphocyte antigen 4 (anti-CTLA-4) human monoclonal antibody (botensilimab) monotherapy and in combination with an anti-programmed cell death protein-1 (PD-1) antibody (balstilimab), and to assess the maximum tolerated dose (MTD) in participants with advanced solid tumors. This study will also determine the recommended phase 2 dose (RP2D) of botensilimab monotherapy and in combination with balstilimab.