Chimeric antigen receptor (CAR)-T cell therapy has been clinically validated as a curative treatment for the difficult to treat malignancies of relapsed/refractory B-cell acute lymphoblastic leukaemia and lymphoma. Here, the CAR-T cells are re-directed towards a single antigen, CD19, which is recognised as a virtually ideal CAR target antigen because it has strong, uniform expression on cancer cells, and is otherwise expressed only on healthy B cells, which are 'dispensable'. Notwithstanding the clinical success of CD19-CAR-T cell therapy, its single specificity has driven therapeutic resistance in 30% or more of cases with CD19-negative leukaemic relapses. Immune checkpoint blockade is also a highly successful cancer immunotherapeutic approach, but it will be less useful for many patients whose malignancies either lack a substantial somatic mutation load or whose tumours are intrinsically resistant. Although CAR-T cell therapy could serve this unmet medical need, it is beset by several major limitations. There is a lack of candidate antigens that would satisfy the requirements for ideal CAR targets. Biological properties such as clonal heterogeneity and micro-environmental conditions hostile to T cells are inherent to many solid tumours. Past clinical studies indicate that on-target, off-tumour toxicities of CAR-T cell therapy may severely hamper its application. Therefore, re-designing CARs to increase the number of antigen specificities recognised by CAR-T cells will broaden tumour antigen coverage, potentially overcoming tumour heterogeneity and limiting tumour antigen escape. Tuning the balance of signalling within bi-specific CAR-T cells may enable tumour targeting while sparing normal tissues, and thus minimise on-target, off-tumour toxicities.