P-CD19CD20-ALLO1 Allogeneic CAR-T Cells in the Treatment of Subjects With B Cell Malignancies

1. Must have signed written, informed consent.

2. Males or females ≥ 18 years of age.

3. Must have prior biopsy proven confirmed diagnosis of DLBCL, FL, MCL, MZL, PMBCL, or CLL.

4. Diagnosis of one of the following:

5. CLL must be documented as CD20-positive.

6. CLL must be documented as active disease meeting ≥ 1 of the following iwCLL 2018 criteria (Hallek, 2018) for requiring treatment:

7. DLBCL, FL, MCL, MZL, or PMBCL must have measurable disease as defined by Lugano 2016 criteria (Cheson, 2016).

8. Must have relapsed/refractory disease as defined by the following:

9. Must be willing to practice birth control from the time of Screening and throughout the first year of the study after P-CD19CD20-ALLO1 administration (both males and females of childbearing potential).

10. Must have a negative serum pregnancy test at Screening and a negative urine pregnancy test within 3 days prior to initiating the lymphodepletion chemotherapy regimen (females of childbearing potential).

11. Must be at least 90 days since ASCT, if performed.

12. Must be at least 4 weeks since autologous CAR-T therapy if such therapy was administered (medical monitor must approve prior CAR T therapy or other prior T cell targeted therapy).

13. Must have adequate vital organ function, defined as follows (or medical monitor approval):

14. Must have recovered from toxicities due to prior therapies to Grade ≤ 2 according to the NCI CTCAE v5.0 criteria or to the subject's prior baseline.

15. Must have an ECOG performance status of 0 to 2.

1. Is pregnant or lactating.

2. Has inadequate venous access.

3. Has active hemolytic anemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), disseminated intravascular coagulation, leukostasis, or amyloidosis.

4. Has an active second malignancy (not disease-free for at least 5 years) in addition to non-Hodgkin lymphoma or CLL, excluding low-risk neoplasms such as non-metastatic basal cell or squamous cell skin carcinoma.

5. Has active autoimmune disease, such as psoriasis, multiple sclerosis, lupus, rheumatoid arthritis, etc. (the medical monitor will determine if a disease is active and autoimmune).

6. Has a history of significant central nervous system (CNS) disease, such as stroke, epilepsy, primary CNS lymphoma, etc. (the medical monitor will determine if significant).

7. Has an active systemic infection (e.g., causing fevers or requiring antimicrobial treatment).

8. Has a history of hepatitis B virus (HBV), hepatitis C virus (HCV), human immunodeficiency virus (HIV), or human T-lymphotropic virus (HTLV) infection, or any immunodeficiency syndrome. Subjects with a history of treated hepatitis C can be enrolled if negative by hepatitis C polymerase chain reaction (PCR) on multiple occasions and with medical monitor approval.

9. Is positive for human herpes virus (HHV)-6 or HHV-7 infection by polymerase chain reaction (PCR) at the Screening Visit (subjects may be included in the study if they are HHV-6 or HHV-7 antibody-positive but PCR-negative).

10. Has New York Heart Association (NYHA) Class III or IV heart failure, unstable angina, or a history of myocardial infarction or significant arrhythmia (e.g., atrial fibrillation, sustained [> 30 seconds] ventricular tachyarrhythmias, etc.).

11. Has any psychiatric or medical disorder (e.g., cardiovascular, endocrine, renal, gastrointestinal, genitourinary, immunodeficiency or pulmonary disorder not otherwise specified) that would, in the opinion of the Investigator or medical monitor, preclude safe participation in and/or adherence to the protocol (including medical conditions or laboratory findings that indicate a significant probability of not qualifying for or being unable to undergo, conditioning chemotherapy and/or CAR-T cell administration).

12. Has received non-mAb anti-cancer medications within 2 weeks of the time of initiating conditioning chemotherapy.

13. Has received mAb therapy within 4 weeks of initiating conditioning chemotherapy.

14. Has received immunosuppressive medications within 2 weeks of the time of administration of P-CD19CD20-ALLO1, and/or expected to require them while on study (the medical monitor will determine if a medication is considered immunosuppressive).

15. Has received systemic corticosteroid therapy ≥ 5 mg/day of prednisone or equivalent dose of another corticosteroid within 1 week or 5 half-lives (whichever is shorter) of the administration of P-CD19CD20-ALLO1 or is expected to require it during the course of the study. (Topical and inhaled steroids are permitted. Systemic corticosteroids are contraindicated after receiving P-CD19CD20-ALLO1 cells outside of study-specific guidance).

16. Has CNS metastases or symptomatic CNS involvement (including leptomeningeal carcinomatosis, cranial neuropathies or mass lesions and spinal cord compression).

17. Has a history of severe immediate hypersensitivity reaction to any of the agents used in this study.

18. Has a history of having undergone allogeneic or xenogeneic transplant, or has undergone autologous transplantation within 90 days.

19. Has received prior allogeneic cellular therapy.

20. History or Grade ≥ 3 HLH/MAS or neurotoxicity with prior therapies (all symptoms of HLH/MAS, neurotoxicity, or CRS from prior therapies must be resolved at the time of enrollment).