Two factors limit the widespread application of traditional donor stem cell transplant: 1) preparing the patient for transplant (conditioning); and 2) graft-versus-host disease (GVHD). Traditional conditioning destroys the recipient's immune system and requires that the marrow transplant be successful because the patient is unable to fight off infection if the donor cells do not survive. GVHD occurs when donor immune cells recognize the recipient's cells as foreign tissue and attack them. Severe GVHD can result in death. This study utilizes a new approach to conditioning which leaves the patient's immune system intact. The transplant product is depleted of GVHD-producing cells but retains tolerance-promoting cells, called facilitating cells, which are intended to ensure the donor and recipient cells coexists peacefully. The toxicity of conditioning and transplantation is significantly reduced. The end result is a marrow system that contains recipient and donor cells, a state called mixed chimerism.