providing an engineered immune cell to the patient, wherein the engineered immune cell comprises an activating receptor and a blocking receptor, each expressed on a surface of the engineered immune cell, said blocking receptor comprising a hinge that comprises a peptide, wherein said peptide comprises a continuous stretch of at least 24 amino acids of SEQ ID NO: 84 derived from a leukocyte immunoglobulin-like receptor subfamily B member 1 (LILRB1), wherein:

when the engineered immune cell encounters a tumor cell, the activating receptor binds to a first ligand on the tumor cell and the activating receptor triggers an activating signal in the engineered immune cell that promotes a cytotoxic response by the engineered immune cell that results in a cytotoxic effect on the tumor cell; and

when the engineered immune cell encounters a normal cell, the activating receptor binds to the first ligand on the normal cell and the blocking receptor binds to a second ligand on the normal cell, wherein the activating receptor triggers the activating signal in the engineered immune cell and the blocking receptor triggers an inhibitory signal in the engineered immune cell that is stronger than the activating signal such that the inhibitory signal dominates and blocks the activating signal from the activating receptor, thereby preventing a localized cytotoxic response by the engineered immune cell.