Chimeric antigen receptor (CAR) T-cells targeting CD19 demonstrate remarkable efficacy in treating B-lineage acute lymphoblastic leukemia (BL-ALL), yet up to 39% of treated patients relapse with CD19(-) disease. We report that CD19(-) escape is associated with downregulation, but preservation, of targetable expression of CD20 and CD22. Accordingly, we reasoned that broadening the spectrum of CD19CAR T-cells to include both CD20 and CD22 would enable them to target CD19(-) escape BL-ALL while preserving their upfront efficacy. We created a CD19/20/22-targeting CAR T-cell by coexpressing individual CAR molecules on a single T-cell using one tricistronic transgene. CD19/20/22CAR T-cells killed CD19(-) blasts from patients who relapsed after CD19CAR T-cell therapy and CRISPR/Cas9 CD19 knockout primary BL-ALL both in vitro and in an animal model, while CD19CAR T-cells were ineffective. At the subcellular level, CD19/20/22CAR T-cells formed dense immune synapses with target cells that mediated effective cytolytic complex formation, were efficient serial killers in single-cell tracking studies, and were as efficacious as CD19CAR T-cells against primary CD19(+) disease. In conclusion, independent of CD19 expression, CD19/20/22CAR T-cells could be used as salvage or front-line CAR therapy for patients with recalcitrant disease.