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Cancer immunotherapies often modulate macrophage effector function by introducing either targeting antibodies that activate Fcγ receptors (FcγRs) or blocking antibodies that disrupt inhibitory SIRPα-CD47 engagement. However, how these competing signals are integrated is poorly understood, raising questions about how to effectively titrate immune responses. Here, we find that macrophage phagocytic decisions are regulated by the ratio of activating ligand to inhibitory ligand over a broad range of absolute molecular densities. Using both endogenous and chimeric receptors, we show that activating:inhibitory ligand ratios of at least 10:1 are required to promote phagocytosis of model antibody-opsonized CD47-inhibited targets and that lowering that ratio reduces FcγR phosphorylation because of inhibitory phosphatases recruited to CD47-bound SIRPα. We demonstrate that ratiometric signaling is critical for phagocytosis of tumor cells and can be modified by blocking SIRPα, indicating that balancing targeting and blocking antibodies may be important for controlling macrophage phagocytosis in cancer immunotherapy.