• Histologically confirmed diagnosis of CD20+ FL (grade 1-3A) or CD20+ MZL (any subtype) (at time of trial entry) with review of the diagnostic pathology specimen at one of the participating institutions. Patients with current histologic transformation are excluded.

• Receipt of at least one prior line of therapy for FL or MZL (with prior treatment including a CD20 monoclonal antibody).

• Measurable disease, defined as ≥1 measurable nodal lesion (long axis \>1.5 cm or short axis \>1.0 cm), or ≥1 measurable extra-nodal lesion (long axis \>1.0 cm), or spleen \>13 cm on PET, CT, or magnetic resonance imaging (MRI). For patients with FL, disease should be FDG-avid based on PET. FDG-avid disease is NOT a requirement for patients with MZL.

• Meets at least one criterion to begin treatment based on the modified GELF (Groupe d'Etude des Lymphomes Folliculaires) criteria:

‣ Symptomatic adenopathy

⁃ Organ function impairment due to disease involvement, including cytopenias due to marrow involvement (WBC \<1.5x109/L; absolute neutrophil count \[ANC\] \<1.0x109/L, Hgb \<10g/dL; or platelets \<100x109/L)

⁃ Constitutional symptoms (defined as persistent fevers \>100.4 F, shaking chills, drenching night sweats, or loss of \>10% of body weight within 6 months)

⁃ Any nodal or extranodal tumor mass \>7 cm in maximum diameter

⁃ \>3 nodal sites of involvement \>3 cm

⁃ Local compressive symptoms or imminent risk thereof

⁃ Splenomegaly (craniocaudal diameter \> 16cm on CT imaging)

⁃ Clinically significant pleural or peritoneal effusion

⁃ Leukemic phase (\>5x109/L circulating malignant cells)

⁃ Rapid generalized disease progression

⁃ Renal infiltration

⁃ Bone lesions

• Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. (Appendix A)

• Age ≥18 years.

• Adequate hematologic and organ function:

∙ Absolute neutrophil count \> 1.0x109/L unless due to marrow involvement by lymphoma in which case ANC must be \>0.5x109/L

‣ Platelets \> 75 x109/L, unless due to marrow involvement by lymphoma, in which case platelets must be \>50 x109/L

‣ Estimated CrCl (based on Cockcroft Gault or MDRD) ≥ 45ml/min or ≥ 45ml/min/1.73m2

‣ Total bilirubin \< 1.5 X ULN, unless Gilbert syndrome, in which case direct bilirubin must be \< 1.5 x ULN

‣ AST/ALT \< 2.5 X ULN, unless documented liver involvement by lymphoma, in which case AST/ALT must be \<5 x ULN

• Ability to understand and the willingness to sign a written informed consent document.

• Willingness to provide a pre-treatment tumor sample by core needle or excisional surgical biopsy. A fresh biopsy is strongly encouraged, but an archival sample is acceptable if it is collected within 90 days and without intervening treatment and the following provisions are met: 1) availability of a tumor-containing formalin-fixed, paraffin-embedded (FFPE) tissue block, 2) if the tumor containing FFPE tissue block cannot be provided in total, sections from this block should be provided that are freshly cut and mounted on positively-charged glass slides. Preferably, 25 slides should be provided; if not possible, a minimum of 15 slides is required. Exceptions to this criterion may be made with approval of the Sponsor-Investigator.

• Willingness to remain abstinent (1) or to use two effective contraceptive methods that result in a failure rate of \<1% per year from screening until: (a) at least 12 months after pre-treatment with rituximab, 12 months after the last dose of epcoritamab, or 3 months after the last dose of zanubrutinib, whichever is longer, if the patient is a male or (b) until at least 12 months after pre-treatment with rituximab, 12 months after the last dose of epcoritamab, or 3 months after the last dose of zanubrutinib, whichever is longer, if patient is a female. Examples of contraceptive methods with a failure rate of \<1% per year include:

‣ Tubal ligation, male sterilization, hormonal implants, established proper use of hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices.

⁃ Alternatively, two methods (e.g., two barrier methods such as a condom and a cervical cap) may be combined to achieve a failure rate of \<1% per year. Barrier methods must always be supplemented with the use of a spermicide.

• True abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject. In contrast, periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception.