As systemic inflammation, tissue damage, autoimmunity and morbidity were not evident in HER2 TG mice, despite abundant HER2 expression in the cerebellum, we conclude that the enhancement of STAT5 signalling limits “on‐target off‐tumour” toxicities by promoting the specific homing of CAR T cells to CXCL9/10‐expressing tumours. The gene discussed is ERBB2; the disease is neoplasm.