Ex-vivo Expanded Donor Regulatory T Cells for Prevention of Acute Graft-Versus-Host Disease

Inclusion Criteria: * Signed informed consent * Diagnoses: a. Hematologic malignancies - Acute myelogenous leukemia (AML), acute lymphoblastic leukemia (ALL), myelodysplastic syndrome (MDS), chronic lymphocytic leukemia (CLL), non-Hodgkin lymphoma (NHL), Hodgkin lymphoma (HL), multiple myeloma (MM) - in complete remission (CR). Complete remission is defined per morphologic, cytogenetic, FISH, molecular, and radiographic imaging studies appropriate for each condition listed. * AML, ALL: Normal values for absolute neutrophil count (\>1000/microL) and platelet count (\>100,000/microL); Absence of extramedullary leukemia; Less than 5 percent blast cells present in the bone marrow * MDS: Bone marrow with ≤5 percent myeloblasts with normal maturation of all cell lines; Peripheral blood demonstrates hemoglobin ≥11 g/dL, platelets ≥100 x 10\^9/L, neutrophils ≥1 x 10\^9/L, and no circulating blasts * CLL: Absence of constitutional symptoms attributable to CLL; No lymph nodes \>1.5 cm in diameter on computed tomography; No hepatomegaly or splenomegaly by computed tomography; Absolute neutrophil count \>1500/microL; Platelet count \>100,000/microL; No clonal lymphocytes in the peripheral blood by immunophenotyping; Bone marrow with no evidence of clonal CLL (by flow cytometry and/or immunohistochemistry * NHL: No clinical evidence of disease or disease-related symptoms; Typically FDG-avid lymphomas: a post-treatment residual mass of any size is permitted as long as it is PET negative; Variably FDG-avid lymphoma/FDG avidity unknown: all lymph nodes normal size by CT; Spleen and liver non-palpable and without nodules; If pretreatment bone marrow biopsy was positive, repeat bone marrow biopsy must be negative; if morphologically indeterminate, immunohistochemistry should be negative If pretreatment bone marrow biopsy was positive, repeat bone marrow biopsy must be negative; if morphologically indeterminate, immunohistochemistry should be negative * HL: No clinical evidence of disease or disease-related symptoms; A post-treatment residual mass of any size is permitted as long as it is PET negative; Spleen and liver must be non-palpable and without nodules; If a pre-treatment bone marrow biopsy was positive, an adequate bone marrow biopsy from the same site must be cleared of infiltrate; if this is indeterminate by morphology, immunohistochemistry should be negative * MM: Absence of monoclonal protein in serum and urine by immunofixation with no current evidence of soft tissue plasmacytoma; Bone marrow aspirate and biopsy must demonstrate less than 5 percent clonal plasma cells; In patients who lack measurable M proteins in the serum and urine being monitored using the FLC levels, the definition of CR requires a normalization of the free light chain (FLC) ratio in addition to the above criteria * MDS: May have achieved CR through either hypomethylating agent therapy, induction chemotherapy, or other therapy * MDS: Low/intermediate-1 IPSS risk category patients are eligible only if they have failed prior therapy or are transfusion-dependent * Peripheral blood white blood count (WBC) greater than 2,000 per microliter (required for collection of dendritic cell precursors) * Adequate vital organ function: Left ventricular ejection fraction (LVEF) ≥ 45% by multigated acquisition (MUGA) scan or echocardiogram; Forced expiratory volume in one second (FEV1), forced vital capacity (FVC), and diffusing lung capacity oxygenation (DLCO) ≥ 50% of predicted values on pulmonary function tests; Transaminases (AST, ALT) \< 3 times upper limit of normal values; Creatinine clearance ≥ 50cc/min * Infectious disease criteria: * No active infection; infection controlled with antimicrobial therapy is not excluded * HIV negative by ELISA or reverse transcription polymerase chain reaction (RT-PCR) \[if ELISA is positive and RT-PCR is negative, the ELISA is considered false positive\] * Hepatitis B and C negative by serology or RT-PCR * Must complete full screening panel: HIV 1, 2 serology and RT-PCR; human T cell lymphotropic virus types 1/2 (HTLV-1/2) serology; rapid plasma reagin (RPR) serology; Epstein-Barr virus (EBV) serology; Cytomegalovirus (CMV) serology; herpes simplex virus (HSV) serology; Varicella-. Zoster Virus (VZV) serology * Performance status: Karnofsky Performance Status Score ≥ 60%. * Agreement to utilize effective contraceptive methods during the study (for one year) * Eligible donors will include siblings age ≥ 18 matched with the recipient at HLA-A, B, C, and DRB1 Exclusion Criteria: * Antithymocyte globulin (ATG) as part of the conditioning regimen