A method of inducing phagocytosis of a target cell, the method comprising: contacting a target cell with a macrophage in the presence of a composition for increasing phagocytosis of a target cell, the composition comprising: (a) an anti-MHC Class I/leukocyte immunoglobulin-like receptor subfamily B member 1 (LILRB1) agent that reduces the binding between MHC Class I on the target cell and LILRB1 on a phagocytic cell, wherein said anti-MHC Class I/LILRB agent is: (i) an anti-MHC Class I antibody, (ii) a LILRB1 peptide that comprises one or more of the extracellular immunoglobulin domains of LILRB1, (iii) an anti-LILRB1 antibody, or (iv) a soluble MHC Class I complex that binds to LILRB1; and (b) an anti-CD47/SIRPA agent that reduces the binding of CD47 on the target cell to SIRPα on a phagocytic cell, wherein said anti-CD47/SIRPA agent is: (i) an anti-CD47 antibody, (ii) a high affinity SIRPα polypeptide that comprises a d1 domain of human SIRPα, with at least one amino acid change relative to the wild-type sequence within the d1 domain, wherein the amino acid change increases the affinity of the SIRPα polypeptide binding to CD47 by decreasing the off-rate by at least 10-fold, (iii) a SIRPA reagent that comprises at least the d1 domain of SIRPA, (iv) an anti-SIRPa antibody, or (v) a soluble CD47 polypeptide, for a period of time sufficient to induce phagocytosis of the target cell by the macrophage, wherein the contacting is in vitro or ex vivo. (a) an anti-MHC Class I/leukocyte immunoglobulin-like receptor subfamily B member 1 (LILRB1) agent that reduces the binding between MHC Class I on the target cell and LILRB1 on a phagocytic cell, wherein said anti-MHC Class I/LILRB agent is: (i) an anti-MHC Class I antibody, (ii) a LILRB1 peptide that comprises one or more of the extracellular immunoglobulin domains of LILRB1, (iii) an anti-LILRB1 antibody, or (iv) a soluble MHC Class I complex that binds to LILRB1; and (i) an anti-MHC Class I antibody, (ii) a LILRB1 peptide that comprises one or more of the extracellular immunoglobulin domains of LILRB1, (iii) an anti-LILRB1 antibody, or (iv) a soluble MHC Class I complex that binds to LILRB1; and (b) an anti-CD47/SIRPA agent that reduces the binding of CD47 on the target cell to SIRPα on a phagocytic cell, wherein said anti-CD47/SIRPA agent is: (i) an anti-CD47 antibody, (ii) a high affinity SIRPα polypeptide that comprises a d1 domain of human SIRPα, with at least one amino acid change relative to the wild-type sequence within the d1 domain, wherein the amino acid change increases the affinity of the SIRPα polypeptide binding to CD47 by decreasing the off-rate by at least 10-fold, (iii) a SIRPA reagent that comprises at least the d1 domain of SIRPA, (iv) an anti-SIRPa antibody, or (v) a soluble CD47 polypeptide, for a period of time sufficient to induce phagocytosis of the target cell by the macrophage, wherein the contacting is in vitro or ex vivo. (i) an anti-CD47 antibody, (ii) a high affinity SIRPα polypeptide that comprises a d1 domain of human SIRPα, with at least one amino acid change relative to the wild-type sequence within the d1 domain, wherein the amino acid change increases the affinity of the SIRPα polypeptide binding to CD47 by decreasing the off-rate by at least 10-fold, (iii) a SIRPA reagent that comprises at least the d1 domain of SIRPA, (iv) an anti-SIRPa antibody, or (v) a soluble CD47 polypeptide,