Isolated cells are described that are not embryonic stem cells, not embryonic germ cells, and not germ cells. The cells can differentiate into at least one cell type of each of at least two of the endodermal, ectodermal, and mesodermal lineages. The cells do not provoke a harmful immune response. The cells can modulate immune responses. As an example, the cells can suppress an immune response in a host engendered by allogeneic cells, tissues, and organs. Methods are described for using the cells, by themselves or adjunctively, to treat subjects. For instance, the cells can be used adjunctively for immunosuppression in transplant therapy. Methods for obtaining the cells and compositions for using them also are described.