Inclusion Criteria:

• Patients 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 hematopoietic stem cell transplant (HSCT) or with a B cell malignancy except those treatable with autologous transplant will be included
• Aggressive non-Hodgkin lymphomas (NHLs) and Other Histologies Such as Diffuse large B cell NHL
• Patients with primary refractory or relapsed disease not eligible for an autologous transplant
• Patients are eligible following an autologous transplant in remission or in relapse
• Planned tandem transplant is allowed for patients at high risk of relapse
• Low grade NHL with < 6 months duration of complete remission (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 be refractory to fludarabine
• Hodgkin disease (HD) - Must have received and failed frontline therapy; patients must have had a prior autologous transplant or were not eligible for autologous transplant; planned tandem transplants are allowed for patients at high risk of relapse
• Multiple myeloma (MM) - Must have received prior chemotherapy and a prior autologous transplant, unless autologous transplant was not possible; planned tandem transplants are allowed for patients at high risk of relapse
• Acute myeloid leukemia (AML) - Must have < 5% marrow blasts at the time of transplant
• Acute lymphocytic leukemia (ALL) - Must have < 5% blasts at the time of transplant
• Chronic myeloid leukemia (CML) - Patients will be accepted beyond chronic phase 1 (CP1) if they have received previous myelosuppressive chemotherapy or HSCT, and have < 5% marrow blasts at time of transplant
• Myelodysplastic (MDS)/Myeloproliferative disorders - Must have failed previous myelosuppressive chemotherapy or HSCT, and have < 5% marrow blasts at time of transplant
• Waldenstrom's Macroglobulinemia - Must have failed 2 courses of therapy
• Patients < 12 years old must be approved by the Fred Hutchinson Cancer Research Center (FHCRC) principal investigator (PI)
• Patients who refuse 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 FHCRC and the FHCRC PI
• Patients with related or unrelated donors for whom
• The best available match is a HLA class II DRB1 and DQB1 matched donor incompatible for any single serologically detectable class I HLA-A, -B, -C mismatch; one additional allele level class I mismatch is allowed OR any combination of 2 allele level mismatches (if typed at the molecular level)
• There is a likelihood of rapid disease progression while HLA typing and results of a preliminary search and the donor pool suggests that a 10/10 HLA-A, B, C, DRB1 and DQB1 matched unrelated donor will not be found
• There is no HLA-A, -B or -C one locus allelic mismatched related donor available
• There is no indication for an autologous transplantation as a treatment option
• DONOR: Related or unrelated donors who are matched for HLA-DRB1 and DQB1 alleles (must be defined by high resolution typing), and who are mismatched for:
• Any single serologically detectable HLA-A or B or C antigen +/- 1 allele or
• Any combination of two HLA-A, -B, or -C alleles (if prospectively typed at molecular level)

Exclusion Criteria:

• Patients who are homozygous at the mismatched major histocompatibility complex (MHC) class I locus
• A positive cross-match exists between the donor and recipient
• Patients with rapidly progressive intermediate or high grade NHL
• Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with AML, ALL or CML
• Life expectancy severely limited by diseases other than malignancy
• Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy
• Fertile men or women unwilling to use contraceptives during and for up to 12 months post treatment
• Female patients who are pregnant or breast-feeding
• Human immunodeficiency virus (HIV) positive patients
• 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
• Fungal infections with radiological progression after receipt of amphotericin B or active triazole for greater than 1 month
• Patients with active bacterial or fungal infections unresponsive to medical therapy
• Patients with the following organ dysfunction symptomatic coronary artery disease or ejection fraction < 35% or other cardiac failure requiring therapy; ejection fraction is required if the patient is > 50 years of age, or history of cardiac disease or anthracycline exposure
• Diffusion capacity of carbon monoxide (DLCO) < 35%; total lung capacity (TLC) < 35%; or forced expiratory volume in one second (FEV1) < 35% and/or receiving supplementary continuous oxygen
• Patients with clinical or laboratory evidence of liver disease would be evaluated for the cause of liver disease, its clinical severity in terms of liver function, bridging fibrosis, and the degree of portal hypertension; patients will be excluded if they are 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 >3 mg/dL; or symptomatic biliary disease
• Patients with poorly controlled hypertension on multiple antihypertensives
• Karnofsky score < 70
• Lansky-Play Performance Score < 50
• DONOR: Bone marrow (BM) donors
• DONOR: Donors who are HIV-positive and/or, medical conditions that would result in increased risk for granulocyte colony-stimulating factor (G-CSF) mobilization and harvest of peripheral blood stem cell (PBSC)
• DONOR: Donors < 12 years of age