Allogeneic Hematopoietic Cell Transplantation for Peripheral T Cell Lymphoma

Background: * Mature neoplasms of T and/or natural killer cells, collectively called peripheral T-cell lymphomas (PTCL), are often poorly responsive to chemotherapy and therefore associated with significant morbidity and mortality. * Allogeneic hematopoietic cell transplantation (HCT) has the potential to cure PTCL but the optimal approach to HCT for these diseases requires ongoing investigation Objectives: * For subjects on the reduced-intensity conditioning (RIC/mRIC) arms, to estimate the progression-free survival * For subjects on the immunosuppression-only conditioning (IOC) and ATL/RIC arms, because they are high risk patients, to preliminarily estimate the proportion who are progression free at one year. Eligibility: * Patients age \>= 12 years * PTCL that is relapsed or refractory to prior therapy and/or PTCL of a risk score where upfront allo HCT in first remission is reasonable (PIT score of intermediate-low risk or higher or supported by clinical practice guidelines1) * At least one potentially suitable 7-8/8 HLA-matched related or unrelated donor (at HLA A, B, C, and DR), or an HLA-haploidentical related donor * Adequate end-organ function * Not pregnant or breastfeeding Design: * There will be four recipient treatment arms that vary in approach, although all with the same backbone of conditioning and GVHD prophylaxis: * Immunosuppression-only conditioning (IOC) arm for high-risk subjects * Reduced-intensity conditioning (RIC) arm for those deemed not high-risk and able to tolerate RIC and without adult T cell leukemia/lymphoma (ATL) * mRIC arm for patients eligible for the RIC arm, as a modified expansion upon completion of the RIC arm * ATL-RIC arm for patients with a diagnosis of ATL * IOC arm: equine anti-thymocyte globulin (e-ATG) 40 mg/kg/day IV on days -14 and -13, pentostatin 4 mg/m2/day IV on days -9 and -5, low-dose cyclophosphamide (5 mg/kg) orally daily on days -9 through -2 --Subjects will be assigned to the IOC arm if there is significant end-organ dysfunction present and it is felt that a conditioning regimen that includes busulfan would likely be associated with intolerable or life-threatening toxicities for the patient. Patients will also be assigned to the IOC arm if they possess a DNA repair defect, telomere maintenance defect, or familial cancer predisposition syndrome that necessitates limiting chemotherapy as much as possible to prevent future cancer risk. * RIC arm: e-ATG 40 mg/kg/day IV on days -14 and -13, pentostatin 4 mg/m2/day IV on days -11 and -7, low-dose cyclophosphamide (5 mg/kg) orally daily on days -11 through - 4; busulfan IV, pharmacokinetically dosed, on days -3 and -2. * mRIC arm: e-ATG 40 mg/kg/day IV on days -14 and -13, pentostatin 4 mg/m2/day IV on days -11 and -7, low-dose cyclophosphamide (5 mg/kg) orally daily on days -11 through - 4; busulfan IV, pharmacokinetically dosed, on days -3 and -2, filgrastim or biosimilar drug 5 mcg/kg/day subcutaneous on days -12, -8, and -4. * ATL-RIC arm: e-ATG 40 mg/kg/day IV on days -14 and -13, pentostatin 4 mg/m2/day IV on days -11 and -7, low-dose cyclophosphamide (5 mg/kg) orally daily on days -11 through -4; busulfan IV, pharmacokinetically dosed, on days -3 and -2, filgrastim or biosimilar drug 5 mcg/kg/day subcutaneous on days -12, -8, and -4, ruxolitinib 45 mg/day from day -12 through day -2, and zidovudine 300 mg orally three times a day from day -1 through day +50. * Peripheral blood stem cells are the preferred graft source, although bone marrow is permitted * GVHD prophylaxis: Post-transplantation cyclophosphamide (PTCy) on days +3 and +4 (50 mg/kg/day on RIC arm, mRIC, and ATL-RIC arms and 25 mg/kg/day on the IOC arm, with the option of 25 mg/kg/day on the RIC arm). Sirolimus on days +5 through +60 (RIC arm, mRIC arm, IOC arm). Patients with somatic mutations in the Akt/mTOR pathway may receive tacrolimus days +5 through +60 instead of sirolimus on the RIC, mRIC, or IOC arms. Mycophenolate mofetil (MMF) on days +5 through +25 on the RIC, IOC, and mRIC arms; MMF will not be given on the ATL-RIC arm. Patients on the ATL-RIC arm will receive tacrolimus on days +5 through +50 and ruxolitinib 15 mg/day from days +5 through +35, 10 mg/day from days +36 through +60, and 5 mg/day from days +61 through +70.