Chimeric antigen receptor (CAR) costimulatory domains derived from native immune receptors steer the phenotypic output of therapeutic T cells. We constructed a library of CARs containing ~2300 synthetic costimulatory domains, built from combinations of 13 signaling motifs. These CARs promoted diverse human T cell fates, which were sensitive to motif combinations and configurations. Neural networks trained to decode the combinatorial grammar of CAR signaling motifs allowed extraction of key design rules. For example, non-native combinations of motifs that bind tumor necrosis factor receptor-associated factors (TRAFs) and phospholipase C gamma 1 (PLCγ1) enhanced cytotoxicity and stemness associated with effective tumor killing. Thus, libraries built from minimal building blocks of signaling, combined with machine learning, can efficiently guide engineering of receptors with desired phenotypes.