Cell engineering strategies to provide allogeneic CAR T cells in the posttransplant setting. (A) Dual TCR/CAR T cell: The TCR may be alloreactive (DLI) or virus-specific (VST). There is a risk of signaling overload in bispecific T cells. (B) TCR-less CAR T cell: The endogenous TCR can be disrupted in mature T cells to abrogate GVHD potential (UCART19, TRAC-CAR). (C) Pro-CAR: Mismatched lymphoid progenitors can yield host tolerant CAR T cells, but require successful engraftment, development, and selection (precursor T cells).