This phase II trial studies how well a donor stem cell transplant, treosulfan, fludarabine, and total-body irradiation work in treating patients with blood cancers (hematological malignancies). Giving chemotherapy and total-body irradiation before a donor stem cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient, they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. The donated stem cells may also replace the patient's immune cells and help destroy any remaining cancer cells.

OUTLINE: Patients are assigned to 1 of 2 arms.

ARM A (HIGH DOSE TREOSULFAN): Patients receive high dose treosulfan intravenously (IV) over 120 minutes on days -6 to -4 and fludarabine IV over 60 minutes on days -6 to -2. Patients then undergo total-body irradiation on day -1 and allogeneic hematopoietic stem cell transplantation on day 0. Patients then receive cyclophosphamide IV over 1-2 hours on days 3-4. Beginning on day 5, patients receive cyclosporine IV twice daily (BID) or three times daily (TID) over 1-2 hours or orally (PO) (after 3 months, in the absence of GVHD, cyclosporine tapering will start by 5-10% per week, until drug withdrawal at 6 months post-transplant). Beginning on day 5, patients also receive mycophenolate sodium PO TID or mycophenolate mofetil IV or PO TID until day 35 (may be continued if active GVHD is present). Beginning on day 5, patients also receive filgrastim until the absolute neutrophil count is > 1,000/uL for 3 consecutive days. Additionally, patients undergo bone marrow aspiration and biopsy, and echocardiography at baseline and blood sample collection and computed tomography (CT) or positron emission tomography (PET)/CT on study.

ARM B (LOW DOSE TREOSULFAN): Patients receive low dose treosulfan IV over 120 minutes on days -6 to -4 and fludarabine IV over 60 minutes on days -6 to -2. Patients then undergo total-body irradiation and allogeneic hematopoietic stem cell transplantation, and receive cyclophosphamide, cyclosporine, mycophenolate sodium or mycophenolate mofetil, and filgrastim as in Arm A. Additionally, patients undergo bone marrow aspiration and biopsy, and echocardiography at baseline and blood sample collection and CT or PET/CT on study.

After completion of transplant, patients are followed up at 28, 56, 84, 365, and 730 days.

Inclusion Criteria:

• Acute leukemia (AL) that includes acute myeloid leukemia (AML) / acute lymphoblastic leukemia (ALL) / mixed phenotype leukemia (MPAL) in complete morphological remission (CR) with or without detectable minimal residual disease (MRD); complete morphological remission is defined by the presence of less than 5% of detectable blasts in bone marrow specimen, evaluated per standard of care. Patients with documented CR but without hematologic recovery since last chemotherapy are considered eligible to the study

• Chronic myelogenous leukemia (CML), except refractory blast crisis. To be eligible in first chronic phase, patients must have failed or be intolerant to at least one tyrosine-kinase inhibitor

• Chronic myelomonocytic leukemia (CMML)

• Myelodysplastic syndromes (MDS)

• Lymphoblastic, Burkitt's and other high-grade lymphoma in any complete (CR) or partial (PR) response

  • CR and PR are defined according to Lugano classification: Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification

• Low grade lymphoma (chronic lymphocytic leukemia [CLL]/small lymphocytic lymphoma [SLL], marginal zone lymphoma, follicular lymphoma) progressed after two treatment regimens, in CR/PR

  • For CLL/SLL, CR and PR are defined according to: International Workshop on CLL (iwCLL) guidelines for diagnosis, indications for treatment, response assessment, and supportive management of CLL
  • CR and PR are defined according to Lugano classification: Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification

• Large cell lymphoma in > second CR (CR2)/ >= PR2

  • CR and PR are defined according to Lugano classification: Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification

• Mantle cell lymphoma, lymphoplasmacytic lymphoma and prolymphocytic leukemia may be eligible after initial therapy if in CR/PR

  • CR and PR are defined according to Lugano classification: Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification
  • For prolymphocytic leukemia (PLL), CR is defined as a normalization of lymphadenopathies (long-axis diameter < 1 cm) and splenomegaly (< 13 cm), absence of constitutional symptoms, PLL cells < 5% in bone marrow and circulating lymphocytes count < 4 x 10^9/L. Patients without hematopoietic recovery are considered eligible to the study. PR is defined as a decrease of >= 30% of the sum of lymphadenopathies' long-axis diameters, a decrease of >= 50% in spleen vertical length beyond normal from baseline, peripheral blood (PB) lymphocytes =< 30 x 10^9/L (and a decrease of >= 50% from baseline)

• Hodgkin Lymphoma in > CR2/PR2

  • CR and PR are defined according to Lugano classification: Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification

• Subjects must be >= 6 months old

• Karnofsky >= 70 or Eastern Cooperative Oncology Group (ECOG) 0-1 (for adults)

• Lansky score >= 50 (for children)

• Adequate cardiac function defined as absence of decompensated congestive heart failure or uncontrolled arrhythmia AND left ventricular ejection fraction >= 40% or shortening fraction > 22%

• Adequate pulmonary function defined as absence of oxygen (O2) requirements and one of the following:

  • Diffusion capacity of the lung for carbon monoxide (DLCO) corrected >= 70% mm Hg
  • DLCO corrected between 60% - 69% mm Hg and partial pressure of oxygen (pO2) >= 70 mm Hg
  • DLCO corrected between 50% - 59% mm Hg and pO2 >= 80 mm Hg Pediatric patients unable to perform pulmonary function tests must have O2 saturation >= 92% on room air. May not be on supplemental oxygen

• Total bilirubin < 2 x upper limit of normal (ULN) unless felt to be related to Gilbert's disease or hemolysis

• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x ULN

• Alkaline phosphatase =< 5 x ULN

• Creatinine < 2.0 mg/dl (adults) or estimated creatinine clearance > 40 ml/min (pediatrics)

  • All adults with a creatinine > 1.2 or a history of renal dysfunction must have estimated creatinine clearance > 40 ml/min

• If recent mold infection, e.g., aspergillus, must be cleared by infectious disease to proceed

• Patients who have undergone prior allogeneic hematopoietic cell transplant are eligible, but the prior transplant must have been performed at least 3 months prior to enrollment, unless in case of graft failure from the prior transplant

• Written and signed informed consent

• DONOR: Donors must be haploidentical relatives of the patients. Donor-recipient compatibility will be tested through HLA typing at high resolution for the HLA loci (-A, -B, -C, -DRB1, -DQB1). Donor and recipient should share at least 5/10 HLA loci

• DONOR: Age >= 12 years

• DONOR: Weight >= 40 Kg

• DONOR: Ability of donors younger than 18 years of age to undergo apheresis without use of a vascular access device. Vein check must be performed and verified by an apheresis nurse prior to arrival.

• DONOR: Donor must meet selection criteria as defined by the Foundation of the Accreditation of Cell Therapy (FACT) and will be screened per the American Association of Blood Banks (AABB) guidelines

• DONOR: In case of more available haploidentical donors, selection criteria should include, in this order:

  • For cytomegalovirus (CMV) seronegative recipients, a CMV seronegative donor

  • Red blood cell compatibility

    • Red blood cell (RBC) cross match compatible
    • Minor ABO incompatibility
    • Major ABO incompatibility

Exclusion Criteria:

• Active, uncontrolled, life-threatening viral, bacterial or fungal infection requiring treatment at time of conditioning regiment administration and transplantation
• Presence of a malignancy other than the one for which the transplant is being performed, with an expected survival less than 75% at 5 years
• Pregnant or breastfeeding
• Known hypersensitivity to treosulfan, fludarabine or cyclophosphamide
• Dosing with another investigational agent within 30 days prior to entry in the study
• Central nervous system (CNS) leukemic involvement not clearing with intrathecal chemotherapy and/or cranial radiation prior to initiation of conditioning (day -6)
• DONOR: Since detection of anti-donor-specific-antigen antibodies (anti-DSA) is associated with higher graft rejection rate, patients will be screened for anti-DSA pre-transplant. Patients with DSA mean fluorescent intensity (MFI) < 5000 after desensitization treatment, will be considered eligible to participate in the study. The first 10 subjects enrolled in the trial will be DSA-negative.