Inclusion Criteria:

- The patient must be not eligible for conventional transplants and must have disease
expected to be stable for at least 100 days without chemotherapy

- Patients with hematologic malignancies treatable with HCT will be included:

- Aggressive non-Hodgkin lymphomas (NHL) and other histologies such as Diffuse
Large B-cell NHL: not eligible for autologous HCT, not eligible for conventional
myeloablative HCT, or after failed autologous HCT;

- Low Grade NHL: with < 6 month duration of complete response (CR) between courses
of conventional therapy;

- Mantle Cell NHL: may be treated in first CR;

- Chronic lymphocytic leukemia (CLL): must have failed 2 lines of conventional
therapy and must be refractory to fludarabine (this includes patients who fail
to have a complete or partial response after therapy with a regimen containing
fludarabine [or another nucleoside analog] or experience disease relapse within
12 months after completing therapy with a regimen containing fludarabine [or
another nucleoside analog]);

- Hodgkin's disease (HD): must have received and failed frontline therapy and have
failed or were not eligible for autologous transplant;

- Multiple myeloma (MM): must have received prior chemotherapy or failed
autografting; following a planned autologous transplant [tandem] is allowed;

- Acute myeloid leukemia (AML): must have < 5% marrow blasts at the time of
transplant;

- Acute lymphocytic leukemia (ALL): must have < 5% marrow blasts at the time of
transplant;

- Chronic myelogenous leukemia (CML): Patients will be accepted beyond CP1 if they
have received previous myelosuppressive chemotherapy or HCT, and have < 5%
marrow blasts at time of transplant;

- Myelodysplastic syndrome/myeloproliferative disease (MDS/MPD): must have failed
previous myelosuppressive chemotherapy or HCT, and have < 5% marrow blasts at
time of transplant;

- Waldenstrom's Macroglobulinemia: must have failed 2 courses of therapy

- Patient refuses to be treated on a conventional transplant protocol (for this
inclusion criteria, transplants must be approved by both the participating
institution's patient review committee, such as the Patient Care Conference [PCC] at
the Fred Hutchinson Cancer Research Center [FHCRC], and the FHCRC principal
investigator)

- Patient with related or unrelated donors for whom:

- There is a likelihood of disease progression while HLA typing and results of a
preliminary search and the donor pool suggest that a 10/10 HLA-A, B, C, DRB1 and
DQB1 matched unrelated donor will not be found;

- Patient and donor must be matched for at least one DRB1 allele and one DQB1
allele;

- Best available matches are HLA class I HLA-A, -B, -C allele matched donors
allowing for any one or two DRB1 and/or DQB1 antigen/allele mismatch;

- There is no indication for an autologous transplantation as a treatment option

- DONOR: For HLA matching inclusion criteria, see Patient Inclusion Criteria

- DONOR: Only peripheral blood stem cells (PBSC) will be permitted as a HSC source on
this protocol

Exclusion Criteria:

- Positive crossmatch between donor and recipients

- Patient's life expectancy is severely limited by diseases other than malignancy

- Patient has central nervous system (CNS) involvement with disease refractory to
intrathecal chemotherapy

- Presence of circulating leukemic blasts (in the peripheral blood) detected by
standard pathology for patients with AML, ALL or CML

- Patient is a fertile man or woman unwilling to use contraceptives during and for up
to 12 months post treatment

- Patient is a female who is pregnant or breastfeeding

- Patient is human immunodeficiency virus (HIV) positive

- Patients with active non-hematologic malignancies (except non-melanoma skin cancers)

- Patients with a history of non-hematologic malignancies (except non-melanoma skin
cancers) currently in a complete remission, who are less than 5 years from the time
of complete remission, and have a > 20% risk of disease recurrence

- Patient has a fungal infection with radiological progression after receipt of
amphotericin B or active triazole for greater than 1 month

- Patient has the following organ dysfunction:

- Symptomatic coronary artery disease or ejection fraction < 35% or other cardiac
failure requiring therapy (ejection fraction is required if age > 50 years or if
the patient has a history of anthracyclines or history of cardiac disease);

- Diffusion capacity of the lung for carbon monoxide (DLCO) < 35% total lung
capacity (TLC) < 35%, forced expiratory volume of the lung in one second (FEV1)
< 35% and/or receiving supplementary continuous oxygen; the FHCRC study
principal investigator (PI) must approve enrollment of all patients with
pulmonary nodules;

- Liver function abnormalities: Patient with clinical or laboratory evidence of
liver disease will be evaluated for the cause of liver disease, its clinical
severity in terms of liver function, bridging fibrosis, and the degree of portal
hypertension

- The patient will be excluded if he/she is found to have fulminant liver failure,
cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis,
esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy;

- Uncorrectable hepatic synthetic dysfunction evinced by prolongation of the
prothrombin time, ascites related to portal hypertension, bacterial or fungal liver
abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin >
3mg/dL, or symptomatic biliary disease

- Patient has poorly controlled hypertension and on multiple antihypertensives

- Karnofsky Performance Score < 70 for adult patients

- Lansky Play-Performance Score < 70 for pediatric patients

- Patient received cytotoxic agents for "cytoreduction" within three weeks (or the
interval in which a cycle of standard chemotherapy would be administered in a
non-transplant setting) prior to initiating the nonmyeloablative transplant
conditioning (exceptions are hydroxyurea and imatinib mesylate)

- DONOR: Marrow donors

- DONOR: Positive crossmatch between donor and recipient

- DONOR: Donor is HIV-positive and/or has a medical condition that would result in
increased risk for G-CSF mobilization and harvest of PBSC

- DONOR: Donor age < 12 years