Methods are provided for treatment of hematologic cancers, particularly lymphomas and leukemias, including without limitation myelogenous and lymphocytic leukemias. A combination of antibodies specific for CD47; and specific for a cancer associated cell surface marker are administered to the patient, and provide for a synergistic decrease in cancer cell burden. The combination of antibodies may comprise a plurality of monospecific antibodies, or a bispecific or multispecific antibody. Markers of interest include without limitation, CD20, CD22, CD52, CD33; CD96; CD44; CD123; CD97; CD99; PTHR2; and HAVCR2.