Compositions and methods of transplanting cells by grafting strategies into solid organs (especially internal organs) are provided. These methods and compositions can be used to repair diseased organs or to establish models of disease states in experimental hosts. The method involves attachment onto the surface of a tissue or organ, a patch graft, a “bandaid-like” covering, containing epithelial cells with supporting early lineage stage mesenchymal cells. The cells are incorporated into soft gel-forming biomaterials prepared under serum-free, defined conditions comprised of nutrients, lipids, vitamins, and regulatory signals that collectively support stemness of the donor cells. The graft is covered with a biodegradable, biocompatible, bioresorbable backing used to affix the graft to the target site. The cells in the graft migrate into and throughout the tissue such that within a couple of weeks they are uniformly dispersed within the recipient (host) tissue. The mechanisms by which engraftment and integration of donor cells into the organ or tissue involve multiple membrane-associated and secreted forms of MMPs.