Genetically Modified T-cells (CMV-Specific CD19-CAR T-cells) Plus a Vaccine (CMV-MVA Triplex) Following Stem Cell Transplantation for the Treatment of Intermediate or High Grade B-cell Non-Hodgkin Lymphoma

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
Life expectancy >= 16 weeks at the time of enrollment

Patients with an indication to be considered for HSCT, who are diagnosed with intermediate or high-grade B cell NHL (e.g., diffuse large B-cell lymphoma [DLBCL], mantle cell lymphoma [MCL], or transformed NHL) in first relapse after achieving complete remission (CR) or did not achieve CR after a first line therapy

Note: COH pathology review should confirm that research participant's diagnostic material is consistent with history of intermediate or high-grade CD19+ malignancy
No known contraindications to myeloablative HSCT, leukapheresis, steroids or tocilizumab, smallpox vaccine and any other modified vaccinia Ankara (MVA)-based vaccines
Patient must be CMV seropositive
Total serum bilirubin =< 2.0 mg/dL
Participants with Gilbert syndrome may be included if their total bilirubin is =< 3.0
Aspartate aminotransferase (AST) < 2.5 x upper limits of normal (ULN)
Alanine aminotransferase (ALT) < 2.5 x ULN
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
Absolute neutrophil count >= 1000/uL (Transfusions and growth factors must not be used to meet this requirement at initial screening)
Hemoglobin (Hb) >= 8 g/dl (Transfusions and growth factors must not be used to meet this requirement at initial screening)
Platelet count >= 50,000/uL (>= 30,000/uL if bone marrow plasma cells are => 50 percent of cellularity) (Transfusions and growth factors must not be used to meet this requirement at initial screening)
Left ventricular ejection fraction >= 45 percent within 8 weeks before enrollment
Oxygen (O2) saturation > 92% without requiring supplemental oxygen
Women of childbearing potential (WOCBP): negative urine or serum pregnancy test
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)

Exclusion Criteria:

Prior autologous/allogeneic stem cell transplant
Growth factors within 14 days of enrollment
Platelet transfusions within 7 days of enrollment
Concurrent use of systemic steroids or chronic use of immunosuppressant medications. Recent or current use of inhaled or topical steroids in standard doses is not exclusionary. Physiologic replacement of steroids (prednisone =< 5 mg /day, or equivalent doses of other corticosteroids) is allowed
Patients with active autoimmune disease requiring systemic immune suppressive therapy are not allowed
Participants may not be receiving any other investigational agents or concurrent biological therapy, chemotherapy, or radiation therapy
Any standard contraindications to myeloablative HSCT per standard of care practices at COH
Subjects with clinically significant arrhythmia or arrhythmias not stable on medical management within two weeks of screening
Subjects with a known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system (CNS), including 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 cerebrospinal fluid [CSF]) will be eligible
History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents or cetuximab
Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia
History of stroke or intracranial hemorrhage within 6 months prior to screening
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 >= 3 years.
Clinically significant uncontrolled illness
Active infection requiring antibiotics
Immunodeficiency virus (human immunodeficiency virus [HIV]) positive
Active viral hepatitis
Females only: Pregnant or breastfeeding
Any other condition that would, in the investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns with clinical study procedures
Procedures (including compliance issues related to feasibility/logistics). Prospective participants who, in the opinion of the investigator, may not be able to comply with all study
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)