CD47 is an antiphagocytic signal that cancer cells employ to inhibit macrophage-mediated destruction. Here, we modified the binding domain of human SIRPα, the receptor for CD47, for use as a CD47 antagonist. We engineered high-affinity SIRPα variants with about a 50,000-fold increased affinity for human CD47 relative to wild-type SIRPα. As high-affinity SIRPα monomers, they potently antagonized CD47 on cancer cells but did not induce macrophage phagocytosis on their own. Instead, they exhibited remarkable synergy with all tumor-specific monoclonal antibodies tested by increasing phagocytosis in vitro and enhancing antitumor responses in vivo. This "one-two punch" directs immune responses against tumor cells while lowering the threshold for macrophage activation, thereby providing a universal method for augmenting the efficacy of therapeutic anticancer antibodies.