Anti-SIRPα antibodies, including multi-specific anti-SIRPα antibodies, are provided, as are related compositions and methods. The antibodies of the disclosure bind to SIRPα and can block the interaction of CD47 on one cell with SIRPα on a phagocytic cell. Antibodies that are bispecific for SIRPα and a second antigen are termed Bi-specific Macrophage Enhancing (BiME) antibodies and have emergent properties. The subject anti-SIRPα antibodies find use in various therapeutic methods. Embodiments of the disclosure include isolated antibodies and derivatives and fragments thereof, pharmaceutical formulations comprising one or more of the anti-SIRPα antibodies; and cell lines that produce the antibodies. Also provided are amino acid sequences of exemplary anti-SIRPα antibodies.