A composition comprising a population of non-immunogenic amnion-derived multipotent progenitor cells (AMP cells) that are epithelial cells that are positive for cytokeratin expression and negative for CD34 expression, in which the population of non-immunogenic AMP cells that are epithelial cells are prepared by the method of: (a) dissociating AMP cells that are epithelial cells from an amniotic membrane of an amnion isolated from a placenta; (b) harvesting the dissociated AMP cells that are epithelial cells; and (c) culturing the collected AMP cells that are epithelial cells in culture medium that contains no animal derived materials other than human proteins; wherein non-immunogenic AMP cells are for use in suppressing, preventing, or enhancing an immune response in a subject who could benefit from it; and in which the immune response: (a) is an autoimmune response such as Type I diabetes, multiple sclerosis, systemic lupus erythematosus, Grave's disease, autoimmune hemolytic anemia, bullous pemphigoid, Hashimoto's thyroiditis, myasthenia gravis, pemphigus, or anemia pernicious; or (b) is an allogeneic response such as graft-versus-host disease or host-graft disease.Una composición que comprende una población de células progenitoras multipotentes derivadas del amnios no inmunogénicas (células AMP) que son células epiteliales que son positivas para la expresión de citoqueratinas y negativas para la expresión de CD34, en la que la población de células AMP no inmunogénicas que son células epiteliales se prepara con el método de: (a) disociar células AMP que son células epiteliales de una membrana amniótica de un amnios aislado de una placenta; (b) recoger las células AMP disociadas que son células epiteliales; y (c) cultivar las células AMP recogidas que son células epiteliales en medio de cultivo que no contiene materiales derivados de animal distintos de proteínas humanas; en la que las células AMP no inmunogénicas son para su uso en la supresión, prevención o mejor