Macrophages hold tremendous promise as effectors of cancer immunotherapy, but the best strategies to provoke these cells to attack tumors remain unknown. Here, we evaluated the therapeutic potential of targeting two distinct macrophage immune checkpoints: CD47 and CD24. We found that antibodies targeting these antigens could elicit maximal levels of phagocytosis when combined together in vitro. However, to our surprise, via unbiased genome-wide CRISPR screens, we found that CD24 primarily acts as a target of opsonization rather than an immune checkpoint. In a series of in vitro and in vivo genetic validation studies, we found that CD24 was neither necessary nor sufficient to protect cancer cells from macrophage phagocytosis in most mouse and human tumor models. Instead, anti-CD24 antibodies exhibit robust Fc-dependent activity, and as a consequence, they cause significant on-target hematologic toxicity in mice. To overcome these challenges and leverage our findings for therapeutic purposes, we engineered a collection of 77 novel bispecific antibodies that bind to a tumor antigen with one arm and engage macrophages with the second arm. We discovered multiple novel bispecifics that maximally activate macrophage-mediated cytotoxicity and reduce binding to healthy blood cells, including bispecifics targeting macrophage immune checkpoint molecules in combination with EGFR, TROP2, and CD71. Overall, our findings indicate that CD47 predominates over CD24 as a macrophage immune checkpoint in cancer, and that the novel bispecifics we created may be optimal immunotherapies to direct myeloid cells to eradicate solid tumors.