Bispecific antibodies (biAbs) used in cancer immunotherapies rely on functional autologous T cells, which are often damaged and depleted in patients with haematological malignancies and in other immunocompromised patients. The adoptive transfer of allogeneic T cells from healthy donors can enhance the efficacy of biAbs, but donor T cells binding to host-cell antigens cause an unwanted alloreactive response. Here we show that allogeneic T cells engineered with a T-cell receptor that does not convert antigen binding into cluster of differentiation 3 (CD3) signalling decouples antigen-mediated T-cell activation from T-cell cytotoxicity while preserving the surface expression of the T-cell-receptor-CD3 signalling complex as well as biAb-mediated CD3 signalling and T-cell activation. In mice with CD19+ tumour xenografts, treatment with the engineered human cells in combination with blinatumomab (a clinically approved biAb) led to the recognition and clearance of tumour cells in the absence of detectable alloreactivity. Our findings support the development of immunotherapies combining biAbs and 'off-the-shelf' allogeneic T cells.