2018-0674 - IL-7 for T-Cell Recovery Post Haplo and CB Transplant - Phase I/II

Inclusion Criteria: * English and non-English speaking patients are eligible. * Patient post a cord blood transplant (CBT) or haplo-SCT, with matched unrelated donors (MUDs), both peripheral blood (PB) and marrow sources with documented absolute neutrophil engraftment * Patients with documented engraftment but require granulocyte-colony stimulating factor (G-CSF) to treat myelosuppression induced by drugs used to treat or prevent infection are eligible * Karnofsky performance status (KPS) \> 60% * Absence of dyspnea or hypoxia (\< 90% of saturation by pulse oximetry on room air) * Bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and/or alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN * Prothrombin time (PT)/partial prothrombin time (PTT) \< 1.5 x ULN * Calculated creatinine clearance \> 60 mL/min/1.73 m\^2 * Diagnosis of acute myeloid leukemia; myelodysplastic syndrome; chronic myeloid leukemia; myelofibrosis or myeloproliferative disease Exclusion Criteria: * Pregnant or nursing * History of lymphoid malignancy (including Hodgkin disease, non-Hodgkin lymphoma, acute lymphoblastic leukemia and chronic lymphocytic leukemia) or acute biphenotypic leukemia * Patients with acute GVHD \> grade 2 at any time during the post-transplant course * Ongoing immunosuppressive therapy for the treatment of GVHD. Patients receiving GVHD prophylaxis will be allowed on this study * History of Epstein-Barr virus (EBV) associated lymphoproliferation * Active uncontrolled viral, bacterial or fungal infection * History of autoimmune disease * Receiving systemic corticosteroid therapy, budesonide is allowed * Uncontrolled hypertension * Corrected QT (QTc) prolongation (QTc \> 470 ms) or prior history of significant arrhythmia or electrocardiogram (ECG) abnormalities * Active drug or alcohol use or dependence that, in the opinion of the investigator, would interfere with adherence to study requirements * Patients with cognitive impairments and/or any past or current psychiatric illness that, in the opinion of the investigator, would interfere with adherence to study requirements or the ability and willingness to give written informed consent