Phase I Study of Sequential Cord Blood Transplants

Inclusion Criteria: Disease Status: NHL, HD, or MM refractory to chemotherapy or relapsed; CLL Rai Stage III/IV, or lymphocyte doubling time of 6 months, or Stage I/II resistant to 2 chemotherapy regimens; AML or ALL in second or subsequent remission or in first remission with adverse cytogenetics or antecedent hematologic disorder Estimated disease-free survival of less than one year ECOG performance status of 0, 1, 2 Lack of 6/6 or 5/6 HLA matched related or 6/6 matched unrelated donor, or a donor is not available within the time frame necessary to perform a potentially curative stem cell transplant 4/6 or greater HLA A, B, CRB1 cord blood units with a combined nucleated cell dose from of > 3.7 x 10(7) NC/kg Exclusion Criteria: Cardiac disease: symptomatic congestive hearth failure or RVG or echocardiogram determined left ventricular ejection fraction of < 45%, active angina pectoris, or uncontrolled hypertension Pulmonary Disease: severe chronic obstructive lung disease, or symptomatic restrictive lung disease, or corrected DLCO of < 50% Renal disease: serum creatinine > 2.0 mg/dl Hepatic disease: serum bilirubin > 2.0 mg/dl (except in the case of Gilbert's syndrome), SGPT or SGOT > 3 x normal Neurologic disease: symptomatic leukoencephalopathy, active DNS malignancy or other neuropsychiatric abnormalities believed to preclude transplantation HIV antibody or Hepatitis B surface antigen positivity Uncontrolled infection Pregnancy or breast-feeding mother