The epigenetic mechanisms that maintain differentiated cell states remain incompletely understood. Here we employed histone mutants to uncover a crucial role for H3K36 methylation in the maintenance of cell identities across diverse developmental contexts. Focusing on the experimental induction of pluripotency, we show that H3K36M-mediated depletion of H3K36 methylation endows fibroblasts with a plastic state poised to acquire pluripotency in nearly all cells. At a cellular level, H3K36M facilitates epithelial plasticity by rendering fibroblasts insensitive to TGFβ signals. At a molecular level, H3K36M enables the decommissioning of mesenchymal enhancers and the parallel activation of epithelial/stem cell enhancers. This enhancer rewiring is Tet dependent and redirects Sox2 from promiscuous somatic to pluripotency targets. Our findings reveal a previously unappreciated dual role for H3K36 methylation in the maintenance of cell identity by integrating a crucial developmental pathway into sustained expression of cell-type-specific programmes, and by opposing the expression of alternative lineage programmes through enhancer methylation.