Resistance to chimaeric antigen receptor (CAR) T cell therapy develops through multiple mechanisms, most notably antigen loss and tumour-induced immune suppression. It has been suggested that T cells expressing multiple CARs may overcome the resistance of tumours and that T cells expressing receptors that switch inhibitory immune-checkpoint signals into costimulatory signals may enhance the activity of the T cells in the tumour microenvironment. However, engineering multiple features into a single T cell product is difficult because of the transgene-packaging constraints of current gene-delivery vectors. Here we describe a cell-sorting method that leverages leucine zippers for the selective single-step immunomagnetic purification of cells co-transduced with two vectors. Such ‘Zip sorting’ facilitated the generation of T cells simultaneously expressing up to four CARs and coexpressing up to three ‘switch’ receptors. In syngeneic mouse models, T cells with multiple CARs and multiple switch receptors eliminated antigenically heterogeneous populations of leukaemia cells coexpressing multiple inhibitory ligands. By combining diverse therapeutic strategies, Zip-sorted multi-CAR multi-switch-receptor T cells can overcome multiple mechanisms of CAR T cell resistance.