This pilot phase I trial studies the side effects of engineered donor stem cell transplant in treating patients with hematologic malignancies. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells (called graft-versus-host disease). Using T cells specially selected from donor blood in the laboratory for transplant may stop this from happening.

PRIMARY OBJECTIVE:

I. To assess the safety of a modified peripheral blood (PB) graft for haploidentical transplantation, obtained by using depletion of naive, cluster of differentiation (CD)45RA+ T cells.

SECONDARY OBJECTIVES:

I. To estimate the proportion of patients with engraftment/graft failure. II. To determine the day 100 and 6 month non-relapse mortality (NRM). III. To estimate the cumulative incidence of grade 2-4 and 3-4 acute graft versus (vs.) host disease (aGVHD).

IV. To assess the rate of chronic GVHD within the first year post transplantation.

V. To assess immune reconstitution and the incidence of infectious episodes. VI. To assess disease response, disease-free survival (DFS) and overall survival (OS) after transplantation.

VII. To compare results with a retrospective cohort of patients treated with bone marrow graft on protocol 2009-0266.

OUTLINE:

Patients receive melphalan intravenously (IV) over 30 minutes on day -6 and fludarabine phosphate IV over 1 hour on days -6 to -3. Patients undergo total-body irradiation (TBI) on day -2 and CD45RA depleted peripheral blood stem cell transplantation on day 0. Patients also receive cyclophosphamide IV over 3 hours on days 3-4. Beginning on day 5, patients receive tacrolimus IV for 2 weeks and orally (PO) for at least 4 months. Beginning on day 7, patients receive filgrastim subcutaneously (SC) daily. Patients with CD20 positive lymphoma may receive rituximab IV on days -13, -6, 1, and 8.

After completion of study treatment, patients are followed up periodically.

Inclusion Criteria:

• Lack of a human leukocyte antigen (HLA) matched related donor, lack of an immediately available 8/8 HLA matched unrelated donor
• Patients must be diagnosed with a high-risk and/or advanced hematologic malignancy defined as one of the following
• Acute lymphocytic leukemia (ALL) in complete remission (CR)1 with high-risk features including adverse cytogenetic such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements; in second or greater morphologic remission; persistent minimal residual disease
• Acute myeloid leukemia (AML) in CR1 with intermediate-risk disease and persistent detectable minimal residual disease (MRD), or with high-risk features defined as: greater than 1 cycle of induction therapy required to achieve remission; preceding myelodysplastic syndrome (MDS) or myeloproliferative disease; presence of FLT3 mutations or internal tandem duplications, DNMT3a, TET2, MLL-partial tandem duplication (PTD), ASXL1, PHF6; FAB M6 or M7 classification; adverse cytogenetics including: -5, del 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8, complex (> 3 abnormalities)
• Patients with AML must have less than 10% bone marrow blasts and < 100/mcL absolute peripheral blood blast count
• Patients with AML in CR2, subsequent CR or with active disease at transplant (< 10% bone marrow blasts)
• MDS with International Prognostic Scoring System (IPSS) intermediate-2 or higher, therapy-related MDS or chronic myelomonocytic leukemia (CMML)
• Aplastic anemia with absolute neutrophil count (ANC) < 1,000 and transfusion dependent after failed immunosuppression therapy
• Chronic myeloid leukemia (CML) >= 1st chronic phase, after failed >=2 lines of tyrosine kinase inhibitors; patients who progressed to blast phase must be in morphologic remission at transplant
• Relapsed Hodgkin's disease or non-Hodgkin's lymphoma (NHL)
• Patients with chemo-sensitive chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) with persistent or recurrent disease after fludarabine-based regimens with < 25% involvement by CLL/SLL cells
• Patients with lymphoblastic lymphoma in remission or after partial response to chemotherapy
• Patients with poor prognosis multiple myeloma by cytogenetics del13, del 17p, t(4;14) or t(14;16) or hypodiploidy, with advanced disease (stage >= 2) and /or relapsed after autologous stem cell transplant
• Zubrod performance status 0-1 or Karnofsky performance status > 70%; patients > 50 years will have to have a Sorror Comorbidity Index =< 3
• Available haploidentical donor willing and eligible to undergo a peripheral blood collection
• Left ventricular ejection fraction (LVEF) > 40%
• Bilirubin =< 1.5 mg/dl (unless Gilbert's syndrome), alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =< 200 IU/ml for adults; conjugated (direct) bilirubin < 2 x upper limit of normal
• Serum creatinine clearance >= 50 ml/min (calculated with Cockcroft-Gault formula)
• Diffusing capacity for carbon monoxide (DLCO) >= 45% predicted corrected for hemoglobin
• Patient or patient's legal representative must provide written informed consent

Exclusion Criteria:

• Human immunodeficiency virus (HIV) positive; active hepatitis B or C
• Patients with active infections; the principal investigator (PI) is the final arbiter of the eligibility
• Liver cirrhosis with greater than grade 1 stage 1 inflammation/fibrosis
• Uncontrolled central nervous system (CNS) involvement by tumor cells within the past 2 months
• History of another primary malignancy that has not been in remission for at least 3 years; (the following are exempt from the 3-year limit: nonmelanoma skin cancer, fully excised melanoma in situ [stage 0], curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on PAP smear)
• Positive beta human chorionic gonadotropin (HCG) test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization
• Inability to comply with medical therapy or follow-up