Chimeric receptors featuring major histocompatibility molecules grafted onto T cell receptor molecules and surrogate co-receptors featuring cell surface receptor ligands fused with signaling molecule domains. The chimeric receptors can be used to redirect cells, altering their specificity. T cells expressing chimeric receptors may bind to ICRs of target T cells for which their chimeric receptors are specific. Surrogate co-receptors may be used to help enhance TCR-CD3 signaling as part of this modular receptor system. The chimeric receptors and surrogate coreceptors may be used to help eliminate autoreactive T cells or program T cells to desired effector functions.