Inclusion Criteria:

- Chemorefractory non-Hodgkin's or Hodgkin's lymphoma or multiple myeloma

- Estimated disease-free survival of less than one year

- 18-74 years of age

- ECOG Performance Status of 0,1 or 2

Exclusion Criteria:

- Patients whose life expectancy is limited by diseases other than their malignancy

- Patients who have a 5/6 or better matched related donor or a 4/6 or better umbilical
cord blood donor and who are medically eligible for conventional myeloablative or
non-myeloablative transplant

- Cardiac disease: symptomatic congestive heart failure or RVG or echocardiogram
determined left ventricular ejection fraction of <30%, active angina pectoris, or
uncontrolled hypertension

- Pulmonary disease: severe chronic obstructive lung disease, or symptomatic
restrictive lung disease, or corrected DLCO of <40% of predicted

- Renal disease: serum creatinine > 3.0mg/dl

- Hepatic disease: serum bilirubin > 3.0mg/dl or alkaline phosphatase, SGOT or SGPT >3x
normal

- Neurologic disease: symptomatic leukoencephalopathy, active CNS malignancy or other
neuropsychiatric abnormalities believed to preclude transplantation

- Uncontrolled infection

- RLI might involve the infusion of circulating tumor cells to the patients. To
minimize the risk, patients who have evidence of circulating tumor cells by light
microscopy and flow cytometry will be excluded

- Patients with acute leukemia