• Age: ≥ 16 years of age with no upper age limit. (NOTE: the first three subjects on this trial must be ≥ 18 years of age.)

• Histologically confirmed aggressive B-cell NHL including the following types defined by World Health Organization (WHO) 2008:

∙ Diffuse Large B-Cell Lymphoma (DLBCL) not otherwise specified; T cell/histiocyte rich large B cell lymphoma; DLBCL associated with chronic inflammation; Epstein Barr Virus (EBV)+ DLBCL of the elderly; OR

‣ Primary mediastinal (thymic) large B cell lymphoma; OR

‣ Transformation to DLBCL; OR

‣ Mantle Cell Lymphoma (MCL).

⁃ 1\. Results of all tests conducted on the tissue at initial diagnosis and/or relapse, including, but not limited to, the MCL subtype (classic and blastoid), Ki-67 proliferation index, and TP53 mutation status should be provided if done. e. Subjects must not have signs or symptoms of CNS disease or detectable evidence of CNS disease on magnetic resonance imaging (MRI) at screening; subjects who have been previously treated for CNS disease, but have no evidence of disease at screening are eligible.

⁃ 3\. Subjects must have disease progression confirmed by either flow cytometry or immunohistochemistry (IHC), disease stabilization, or disease recurrence after at least two lines of therapy.

⁃ a. For DLBCL, the two lines of prior therapy must include an anthracycline and anti-CD20 monoclonal antibody treatment.

⁃ b. For MCL, the two lines of prior therapy include any combination of the agents below:

• an anti-CD20-directed therapy

• BTK inhibitor

• Anthracycline or Bendamustine c. Relapse or refractory after single antigen targeting CAR T cell therapy.

• Must have evaluable or measurable disease according to the revised International Working Group (IWG) Response Criteria for Malignant Lymphoma;34 lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy. MCL patients without measurable nodal or extranodal disease by IWG criteria are eligible if they have bone marrow involvement of MCL.

• Subjects who have undergone autologous stem cell transplantation (SCT) with disease progression or relapse are eligible.

• Subjects who have undergone allogeneic SCT will be eligible if, in addition to meeting other eligibility criteria, are:

∙ At least 100 days post-transplant,

‣ Do not have graft versus host disease (GVHD)

• At least 14 days or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy (including radiation therapy) at the time the subject is planned for leukapheresis, except for systemic inhibitory/stimulatory immune checkpoint therapy, which requires 5 half-lives.

• At least 7 days must have elapsed since any prior steroid use (dexamethasone or prednisone) prior to apheresis. Physiological replacement doses are allowable with no washout period. Topical or inhaled steroids for localized GVHD is allowable.

• Peripheral blood CD3 count must be \>0.15 x 106 cells/mL within 14 days prior to proceeding with apheresis.

⁃ Toxicities from prior therapy must be stable and recovered to ≤ grade 1 (exceptions include non-clinically significant toxicities such as alopecia and the organ function definitions provided in inclusion criteria 12).

⁃ Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, or Karnofsky ≥ 80%.

⁃ Adequate organ function as defined by:

• Absolute neutrophil count (ANC) ≥ 750/μL for DLBCL and ≥ 500/μL for MCL.

∙ Platelet count ≥ 50,000/ μL.

∙ Renal: Creatinine ≤ 2 mg/dL OR creatinine clearance (as estimated by Cockcroft Gault equation) ≥ 60 mL/min.

∙ Hepatic: Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤ 2.5 upper limit of normal (ULN).

∙ Total bilirubin ≤ 1.5 mg/dl, except in subjects with Gilbert's syndrome where a bilirubin \<3.0 will be acceptable.

∙ Cardiac: Ejection fraction ≥ 45%, no evidence of physiologically significant pericardial effusion as determined by an echocardiogram (ECHO), and no clinically significant electrocardiogram (ECG) findings within 6 weeks of apheresis.

∙ Pulmonary: No clinically significant pleural effusion and;

⁃ 1\. Baseline oxygen saturation must be \> 92% on room air and; 2. For screening only and within 6 weeks of apheresis: Pulmonary Function Test: Diffuse capacity of the lungs for carbon monoxide (DLCO), forced expiratory volume in one second (FEV1) and forced vital capacity (FVC) are all ≥50% of predicted by spirometry after correcting for hemoglobin.

⁃ a) Post apheresis: If participant has received bridging therapy or develops a significant illness, retest may be performed per investigator discretion.

⁃ 13\. Females of childbearing potential must have a negative serum pregnancy test (females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be of childbearing potential). 14. Subjects of childbearing or child-fathering potential must be willing to practice birth control from the time of enrollment on this study and for 12 months after receiving the CD19x22 infusion; females of childbearing potential must have a negative pregnancy test.

⁃ 15\. Must be able to give informed consent; subjects unable to give informed consent will not be eligible for this study.