The goal of this clinical research study is to learn if ONC-PluReceptor NK cell therapy (combined with the monoclonal antibody therapies epcoritamab and tafasitamab) can help to control relapsed or refractory B-cell Non-Hodgkin Lymphoma. The safety of this treatment will also be studied.

Primary Objective:

To establish the safety and recommended phase II dose (RP2D) of umbilical cord blood (CB)- derived natural killer (NK) cells transduced with ONC-PluReceptor (CD3 complex/IL-15) in combination with epcoritamab and tafasitamab for patients with relapsed/refractory (R/R) CD19/CD20-positive B-cell non-Hodgkin lymphomas.

Secondary Objectives:

1. To evaluate the overall response rate (ORR), complete response (CR) rate and partial response (PR) rate of patients treated at the RP2D.
2. To evaluate the duration of response (DOR).
3. To evaluate the progression-free survival (PFS) rate.
4. To evaluate the overall survival (OS) time.
5. To quantify the persistence of infused donor NK cells in the recipient.
6. To conduct comprehensive immune reconstitution studies.

Inclusion Criteria:

1. Patients with R/R DLBCL or FL with all of the following:

   Failure of >/= 2 prior lines of therapy, or an autologous or allogeneic stem cell transplant.

   Prior failure of CAR-T or not eligible for CAR-T cells.

2. Tumor biopsy positive for CD19 or CD20 at >/= 1% by immunohistochemistry or flow cytometry.

3. Age 18-80 years.

4. Karnofsky performance status >/=60%.

5. Absolute neutrophil count >/=500/mm3 and platelet count >/=50,000/mm3.

6. Serum creatinine clearance (CrCl) >/=30 ml/min, estimated using the Cockcroft-Gault equation:

   Estimated creatinine clearance = (140-age [years]) x weight (kg) (x Fa) / serum creatinine (mg/dL) x 72 [a where F=0.85 for females and F=1 for males].

7. Adequate hepatic function (ALT and/or AST </=3 x upper limit of normal (ULN); bilirubin and ALP </=2 x ULN). Patients with cancer involvement of the liver and elevation of ALT, AST, bilirubin, and/or ALP </= 5 x ULN are eligible, per PI discretion.

8. Adequate pulmonary function with FEV1, FVC and DLCO (corrected for hemoglobin and volume) >/=50%.

9. Adequate cardiac function with left ventricular ejection fraction >/=40%, and no uncontrolled arrhythmias or symptomatic cardiac disease.

10. If female of child-bearing potential, she must not be pregnant or breastfeeding and required to have a negative urine or serum pregnancy test prior to enrollment.

11. Female participants of non-childbearing potential must meet at least one of the following criteria:

    i. Postmenopausal (no menses in greater than or equal to 12 consecutive months).

    ii. History of hysterectomy or bilateral salpingo-oophorectomy. iii. Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy).

    o Subjects who are of childbearing potential, sexually active, and at risk of pregnancy must agree to use a highly effective method of contraception for the duration of the active treatment and at least 3 months post-completion of the study therapy. See Appendix B. Highly effective methods of contraception include the following:

    iv. Hormonal contraception (i.e., birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

    o Men treated or enrolled in this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of study agent administration. Men who are able to have children must use effective birth control while in the study. If the male participant fathers a child or suspects that he has fathered a child while in the study, he must immediately notify his doctor.

12. Agree to sign the consent to the long-term follow-up protocol PA17-0843 to fulfill the institutional responsibilities to various regulatory agencies

Exclusion Criteria:

1. Lymphoma in CR with no measurable sites of disease.
2. Major surgery <4 weeks prior to first dose of study drug.
3. Any other severe or uncontrolled disease or condition that might increase the risk associated with study participation.
4. Any other malignancy known to be active, with the exception of treated cervical intra-epithelial neoplasia and non-melanoma skin cancer.
5. Grade >/= 3 non-hematologic toxicity from prior therapy that has not improved to grade </= 2.
6. Active hepatitis B, either active carrier (HBsAg +) or viremic (HBV DNA.>/=10,000 copies/mL, or >/=2,000 IU/mL), or hepatitis C (detectable viral load by HCV RNA PCR)
7. Active infection requiring parenteral antibiotics.
8. HIV infection.
9. Treatment within prior 2 weeks with any anti-cancer agent, investigational or approved.
10. Active central nervous system (CNS) involvement (untreated parenchymal brain metastasis or positive cytology of cerebrospinal fluid).
11. Life expectancy \