T cell receptor cross-reactivity allows a fixed T cell repertoire to respond to a much larger universe of potential antigens. Recent work has emphasized the importance of peptide structural and chemical homology, as opposed to sequence similarity, in T cell receptor cross-reactivity. Surprisingly, though, T cell receptors can also cross-react between ligands with little physiochemical commonalities. Studying the clinically relevant receptor DMF5, we demonstrate that cross-recognition of such divergent antigens can occur through mechanisms that involve heretofore unanticipated rearrangements in the peptide and presenting MHC protein, including binding-induced peptide register shifts and extensions from MHC peptide binding grooves. Moreover, cross-reactivity can proceed even when such dramatic rearrangements do not translate into structural or chemical molecular mimicry. Beyond demonstrating new principles of T cell receptor cross-reactivity, our results have implications for efforts to predict and control T cell specificity and cross-reactivity and highlight challenges associated with predicting T cell reactivities.