Here we show that Tmod cells can be designed to target 2-4 antigens to provide different practical and conceptual options for a blood cancer therapy: (i) mono- and bispecific activating receptors that target CD33, a well-known AML antigen expressed on the majority of AML tumors (as well as healthy myeloid cells) and CD43 (SPN), an antigen expressed on many hematopoietic cancers (and normal blood lineages); and (ii) mono- and bispecific inhibitory receptors that target CD16b (FCGR3B) and CLEC9A, antigens expressed on key normal blood cells but not on most blood cancers. Here, FCGR3B is linked to hematopoietic and lymphoid cell neoplasm.