<p>Combination immunotherapy, which integrates immune checkpoint inhibition with immunostimulatory approaches, has emerged as a leading strategy for cancer treatment. However, patient responses vary widely due to cancer heterogeneity. In this work, we develop a mathematical model of cancer–immune interactions that incorporates combination therapy, accounting for both the limited efficacy of immune responses and the impact of immune checkpoint inhibitors. Using a hierarchical bifurcation framework, we derive explicit conditions for equilibrium stability and bifurcations, which delineate distinct clinical outcomes: complete tumor eradication, partial control, oscillatory dynamics, tumor escape, and bistability. We further perform global sensitivity analysis to assess the influence of key parameters on tumor progression and immune activity in oscillatory and partially controlled states. Our findings highlight dual parameter effects, where a single factor can suppress tumor growth in partially controlled states yet destabilize tumor–immune dynamics in oscillatory regimes. Numerical simulations not only corroborate the theoretical results but also uncover critical system features, such as immune delay and suppression. Overall, this study demonstrates the sensitivity of tumor–immune dynamics to parameters and initial conditions, and illustrates how dynamical systems analysis can guide the design of personalized immunotherapy strategies.</p>