Clinical applications of CAR-T cells are limited by the scarcity of tumor-specific targets and are often afflicted with the same on-target/off-tumor toxicities that plague other cancer treatments. A new promising strategy to enforce tumor selectivity is the use of logic-gated, two-receptor systems. One well-described application is termed Tmod™, which originally utilized a blocking inhibitory receptor directed towards HLA-I target antigens to create a protective NOT gate. Here we show that the function of Tmod blockers targeting non-HLA-I antigens is dependent on the height of the blocker antigen and is generally compatible with small, membrane-proximal targets. We compensate for this apparent limitation by incorporating modular hinge units to artificially extend or retract the ligand-binding domains relative to the effector cell surface, thereby modulating Tmod activator and blocker function. By accounting for structural differences between activator and blocker targets, we developed a set of simple geometric parameters for Tmod receptor design that enables targeting of blocker antigens beyond HLA-I, thereby broadening the applications of logic-gated cell therapies.