Pilot/Feasibility Study of CMV-Specific CD19-CAR T Cells Plus CMV-MVA Triplex Following Matched Related Allogeneic Hematopoietic Cell Transplantation for Patients With High-Risk Acute Lymphoblastic Leukemia

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study PI approval * Note: For research participants who do not speak English, a short form consent may be used with a City of Hope (COH) certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated full consent is processed * Age: ≥ 18 years * Karnofsky performance status (KPS) ≥ 70 * Participants with high-risk ALL defined as: * Any complete remission (CR) with minimal residual disease (MRD)+ (by flow cytometry, polymerase chain reaction \[PCR\] or clonoSEQ) at the time of HSCT; or * Blasts ≥ 5% at the time of transplant; or * Complete response (CR)2 or higher irrespective of MRD status; or * Requiring \> 1 regimen to achieve CR1 * Pathology confirmed CD19+ ALL after the last targeted therapy if the patient has active disease or before the last therapy if the patient is in CR * Note: CD19 positivity must be documented in a pathology report; however, it is not a requirement that the CD19 testing be performed by a COH pathologist * Planned allogeneic HSCT (myeloablative or reduced intensity conditioning) according to institutional eligibility requirements with an available 8/8 (HLA A, B, C, DR) allele-matched related is allowed per discretion of the principal investigator. for allogeneic HSCT will be unmanipulated mobilized peripheral blood stem cell (PBSC) or bone marrow * Participants who received other prior forms of CAR T therapy are eligible * No known contraindications to HSCT, leukapheresis, steroids or tocilizum,ab, smallpox vaccine and any other modified vaccinia ankara virus (MVA)-based vaccines * Total serum bilirubin ≤ 2.0 mg/dL (to be performed no more than 45-days prior to hematopoeitic stem cell \[HSC\] infusion unless otherwise stated) * Participants with Gilbert syndrome may be included if their total bilirubin is ≤ 3.0 (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Aspartate aminotransferase (AST) \< 2.5 x upper limit of normal (ULN) (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Alanine aminotransferase \< 2.5 x ULN (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Serum creatinine ≤ 2.5 x ULN or estimated creatinine clearance of ≥ 40 mL/min per the Cockcroft-Gault formula, and the participant is not on hemodialysis (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Cardiac function (12 lead-electrocardiogram \[ECG\]): Corrected QT interval (QTc) must be ≤ 480 msec (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Left ventricular ejection fraction ≥ 45% within 8 weeks before protocol therapy (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Oxygen (O2) saturation \> 92% without requiring supplemental oxygen (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Seronegative for HIV quantitative real time polymerase chain reaction (qPCR), hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis (RPR) (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed OR * If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable * Negative for COVID-19 within 72 hours of day 0 of protocol therapy (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Negative for human herpes virus-6 (HHV6) by PCR-based assay (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Meets other institutional and federal requirements for infectious disease titer requirements (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Participants must have negative QuantiFERON-TB Gold (QFTG) test (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * Participants with positive QFTG test need clearance from ID before protocol therapy * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test (to be performed no more than 45-days prior to HSC infusion unless otherwise stated) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) * DONOR CRITERIA: The identified donor must be the original donor whose stem cells were used for the research participant's alloHSCT * DONOR CRITERIA: Donor must be CMV seropositive through the following: * CMV seropositive AND * CMV positive by CMV insight T cell immunity testing through Viracor (Test code 30360) * DONOR CRITERIA: The donor's hepatitis B surface antigen must be negative and the hepatitis C antibody must be nonreactive. In the case of a positive hepatitis C antibody result, the HCV viral PCR will have to be performed and the results should be negative * DONOR CRITERIA: The donor must be HIV negative * DONOR CRITERIA: KPS ≥ 70 * DONOR CRITERIA: Documented body weight * DONOR CRITERIA: Willingness to sign 'donor consent form' and undergo T cell leukapheresis for the collection of PBMCs for cellular manufacture * DONOR CRITERIA: COH standard operating procedures (SOP) will be used for allogeneic donor evaluation, selection, and consent. * DONOR CRITERIA: The donor is approved and has completed the donor evaluation per institutional guidelines. Additionally, donor will also be screened for the following infectious diseases: * Epstein-Barr virus (EBV) by PCR, * Human herpes virus 6, 7, and 8 (HHV6, HHV7, HHV8) * Parvovirus B19 Note: ID test results for EBV by PCR, HHV6, HHV7, HHV8 and parvovirus B19 are necessary to proceed with the apheresis procedure but do have to be resulted and negative before participant CAR T infusion. Donor screening will be in compliance with all requirements of Food and Drug Administration (FDA) regulation 21 CFR Part 1271 including donor screening for COVID-19 exposure or infection. Exclusion Criteria: * Concurrent use of systemic steroids. Recent or current use of inhaled or topical steroids in standard doses is not exclusionary. Physiologic replacement of steroids (prednisone ≤ 0.5 mg /day, or equivalent doses of other corticosteroids) is allowed * Participants with active autoimmune disease requiring systemic immune suppressive therapy are not allowed * Any contraindications to standard conditioning transplant regimens per standard of care practices at COH * Subjects with clinically significant arrhythmia or arrhythmias not stable on medical management within two weeks of screening * History or prior diagnosis of other immunologic or inflammatory disease affecting the central nervous system (CNS), including uncontrolled seizure disorder, any measurable masses of CNS, or any other active CNS disease. Note: Research participants with a history of CNS disease that has been effectively treated to complete remission (\< 5 white blood cells \[WBC\]/mm\^3 and no blasts in CSF) will be eligible * Participants should not have any uncontrolled illness including symptomatic congestive heart failure, unstable angina pectoris, poorly controlled pulmonary disease, or psychiatric illness/social situations that would limit compliance with study requirements * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * History of stroke or intracranial hemorrhage within 3 months prior to screening * Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia * Participants with uncontrolled seizures * Active viral hepatitis * History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin; non-muscle invasive bladder cancer; malignancy treated with curative intent with no known active disease present for ≥ 2 years * Clinically significant uncontrolled illness * Active infection not responding to antibiotics * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)