Inclusion Criteria:

          -  Histology and immunohistochemistry (CD20+) confirmed Burkitt lymphoma (BL), diffuse
             large B-cell lymphoma (DLBCL), or histology confirmed KSHV-associated multicentric
             Castleman disease with elevated blood KSHV viral load

          -  Cohort 1: Age should be equal to or greater than 15

          -  Cohort 2: Age: 2-15

          -  Measurable disease

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2

          -  Able to provide informed consent (adults) or assent (children < 18 years) in English
             or Luganda

          -  Human immunodeficiency virus (HIV)-infected patients eligible if meet the following
             criteria:

               -  CD4+ T-cell count > 200 cells/uL

               -  HIV treatable with effective antiretroviral therapy that does not include agents
                  with known significant drug-drug interactions with accompanying chemotherapy
                  (ritonavir and cobicistat contraindicated)

        Exclusion Criteria:

          -  Previous therapy for lymphoma or KSHV-multicentric Castleman disease (MCD)

          -  History of hypersensitivity to rituximab

          -  Pregnant or nursing women. Men or women may not participate unless they have agreed to
             use effective contraception during treatment and for 12 months following completion of
             therapy

          -  Inadequate organ function, unless attributed to lymphoma or KSHV-MCD

          -  Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) > 2.5 times upper
             limit of normal

          -  Creatinine > 2 times upper limit than normal or calculated creatinine clearance < 60
             mL/min

          -  New York Heart Association (NYHA) cardiac failure class III or IV

          -  Patients with clinically significant anemia-hemoglobin less than 10 g/dL

          -  Central nervous system (CNS) masses consistent with lymphoma or untreated infection;
             leptomeningeal disease will not be excluded

          -  Patients with malignancy within 5 years, other than resected local skin cancer or
             limited Kaposi sarcoma (KS) (no known pulmonary KS)

          -  Patients with evidence of active infections including malaria and hepatitis B
             (participants with hepatitis B virus [HBV] controlled on antivirals will not be
             excluded)