Inclusion Criteria:

One of these diagnoses:

- Acute myeloid leukemia in complete or partial remission

- Acute lymphocytic leukemia in complete or partial remission

- Chronic myeloid leukemia in first or subsequent chronic phase or accelerated phase

- Chronic lymphocytic leukemia that has recurred or failed after at least one course of
front-line therapy

- Hodgkin's disease or non-Hodgkin's lymphoma that has failed front-line therapy, is in
second or subsequent remission, or is in chemosensitive relapse

- Multiple myeloma that is in complete or partial remission or in chemosensitive
relapse

- Myelodysplastic Syndrome classified as intermediate-2 or high risk according to
International Prognostic Scoring System

- Metastatic renal cell carcinoma that has failed at least one previous front-line
chemotherapy and/or biological therapy regimen and that is radiographically
detectable and evaluable

- Treatment with at least one previous course of chemotherapy or biological therapy for
the malignancy for which allogeneic PBPCT is being considered (i.e., a subject cannot
be enrolled on this study for initial treatment of a malignancy).

AND at least one of the following:

- Age 50 years or older.

- Previous transplant with autologous or allogeneic hematopoietic cells (peripheral
blood, bone marrow, or placental blood).

- High-risk status of hematologic malignancy, i.e., not in first complete remission or
first chronic phase.

- Presence of other medical condition that could place subject at unacceptably high
risk of regimen-related mortality such as documented chronic bronchitis or emphysema;
decreased cardiac ejection fraction (but with ejection fraction at least 30%), or
history of coronary artery disease; renal insufficiency (but with creatinine
clearance at least 30 mL/min); hepatic cirrhosis (but with normal hepatic synthetic
function); or documented or presumed invasive fungal infection requiring treatment
with intravenous antifungal agent(s).

Exclusion Criteria:

- Eligibility for another clinical therapeutic protocol or standard-of-care treatment
that offers higher probability of cure or long-term control of subject's malignancy.

- Progressive Hodgkin's disease, non-Hodgkin's lymphoma, Hodgkin disease or multiple
myeloma that is refractory to salvage chemotherapy.

- Acute leukemia (AML or ALL) in relapse, CML in blast phase/blast crisis, or MDS with
greater than 30% marrow involvement (MDS-AML). Subjects with these disease
characteristics may be considered for this study if complete or partial remissions
(CRs or PRs) occur after salvage chemotherapy.

- Severe organ dysfunction, such as: cardiac ejection fraction below 30% or symptomatic
ischemic cardiac disease; creatinine clearance below 30 mL/min; carbon monoxide
diffusing capacity (DLCO) below 35% and/or need for supplemental oxygen; severe
hepatic cirrhosis with ascites and/or varices; hepatic dysfunction associated with
abnormal synthetic function (e.g., coagulopathy) and/or bilirubin greater than two
times upper limit of normal and/or transaminases (AST or ALT) above four times upper
limit of normal.

- Untreated or progressive central nervous system involvement by malignancy

- Subject is pregnant or breast-feeding.

- Karnofsky score below 50

- Seropositivity for human immunodeficiency virus (HIV).

- Life expectancy less than 12 weeks with conventional treatments.

- For subjects who are fertile, refusal to practice contraception upon entering this
study and for at least 12 months after PBPCT or after cessation of immunosuppressive
treatments (e.g., cyclosporine), whichever occurs later.

- Failure to obtain at least 5.0 x 106 allogeneic donor CD34+ cells per kg of recipient
weight in PBPC product.