 This study will investigate the safety and effectiveness of a modified stem cell transplant procedure for treating cancers of the blood and immune system. Patients with cancers and pre-cancerous conditions originating in blood or immune system cells can sometimes benefit greatly from, and even be cured by, transplants of stem cells cells produced by the bone marrow that mature into blood cells. In addition to producing new bone marrow and restoring normal blood production and immunity, the donated cells fight any residual tumor cells that might have remained in the body, in what is called a graft-versus-tumor effect. 