Inclusion Criteria:

• Participant must be ≥ 18 years of age.
• Participant has a confirmed diagnosis of large B-cell lymphoma (including DLBCL, high-grade B-cell lymphoma [HGBCL], primary mediastinal B-cell lymphoma [PMBCL], etc), FL, MCL, marginal zone lymphoma, transformation of indolent B-cell lymphoma, or lymphoplasmacytic lymphoma, including Waldenstrom macroglobulinemia.
• Participant has relapsed or progressed on at least 2 prior lines of therapy.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
• All participants must have measurable disease via computed tomography (CT), magnetic resonance imaging (MRI), or positron emission tomography (PET)-CT.
• Documented CD19 or CD20 positivity of their B-cell neoplasm based on any representative pathology report from the past 3 months.
• Adequate hematologic, hepatic and renal function.
• All contraceptive use by men and women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.
• Capable of giving signed informed consent.

Exclusion Criteria:

• Known or suspected history of hemophagocytic lymphohistiocytosis (HLH).
• Unresolved toxicities from previous anticancer therapy.
• Primary central nervous system (CNS) lymphoma or known CNS involvement with lymphoma.
• Active medical condition requiring chronic systemic steroid use (>10 mg/day prednisone or equivalent of >140 mg over the last 14 days) or immunosuppressive therapy, within 6 months prior to the first dose of MDX2003.
• Known positivity with human immunodeficiency virus (HIV), known active hepatitis B or C, or uncontrolled chronic or ongoing infection requiring intravenous treatment.
• Participant has a history of allogenic tissue or solid organ transplant, with the exception of corneal transplants.
• Known hypersensitivity to allopurinol or rasburicase.
• Participant has a seizure disorder requiring therapy at the time of screening (such as steroids or anti-epileptics).
• Participant is not suitable for participation, whatever the reason, as judged by the Investigator, including medical or clinical conditions.