Chimeric antigen receptors (CARs) and synthetic Notch (synNotch) receptors are engineered cell-surface receptors that sense a target antigen and respond by activating T cell receptor signaling or a customized gene program, respectively. Here, to expand the targeting capabilities of these receptors, we develop “universal” receptor systems for which receptor specificity can be directed post-translationally via covalent attachment of a co-administered antibody bearing a benzylguanine (BG) motif. A SNAPtag self-labeling enzyme is genetically fused to the receptor and reacts with BG-conjugated antibodies for covalent assembly, programming antigen recognition. We demonstrate that activation of SNAP-CAR and SNAP-synNotch receptors can be successfully targeted by clinically relevant BG-conjugated antibodies, including anti-tumor activity of SNAP-CAR T cells in vivo in a human tumor xenograft mouse model. Finally, we develop a mathematical model to better define the parameters affecting universal receptor signaling. SNAP receptors provide a powerful strategy to post-translationally reprogram the targeting specificity of engineered cells.