This study will investigate the safety and effectiveness of a modified donor stem cell transplantation procedure for treating advanced mycosis fungoides (MF), a lymphoma primarily affecting the skin, and Sezary syndrome (SS), a leukemic form of the disease. Donated stem cells (cells produced by the bone marrow that mature into the different blood components white cells, red cells and platelets) can cure patients with certain leukemias and lymphomas and multiple myeloma. These cells generate a completely new, functioning bone marrow. In addition, immune cells from the donor grow and generate a new immune system to help fight infections. The new immune cells also attack any residual tumor cells left in the body after intensive chemotherapy. However, stem cell transplantation carries a significant risk of death, because it requires completely suppressing the immune system with high-dose chemotherapy and radiation. In addition, lymphocytes from the donor may cause what is called graft vs. host disease (GvHD), in which these cells see the patient s cells as foreign and mount an immune response to destroy them. To try to reduce these risks, patients in this study will be given low-dose chemotherapy and no radiation, a regimen that is easier for the body to tolerate and involves a shorter period of complete immune suppression. In addition, a monoclonal antibody called Campath-1H will be given to target lymphocytes, including those that have become cancerous.