Inclusion Criteria:

          -  Clinically eligible to receive Food and Drug Administration (FDA) approved standard of
             care combination immune checkpoint therapy with ipilimumab and nivolumab for
             unresectable stage III or stage IV melanoma.

          -  No therapy with immune checkpoint inhibitors within 1 year prior to starting
             combination checkpoint therapy. Prior adjuvant ipilimumab, nivolumab, or pembrolizumab
             as single agent is allowed if greater than 1 year since last treatment and patient had
             no grade 3 or 4 toxicities from the checkpoint inhibitors. History of adjuvant
             interferon is allowed.

          -  Obtained within one week prior to randomization:

               -  White blood count ≥ 3,000/µL

               -  Absolute neutrophil count (ANC) ≥ 1,500/µL

               -  Platelet count ≥ 100,000/µL

               -  Hemoglobin ≥ 9 g/dL

               -  Serum creatinine ≤ 1.5 x institutional upper limit of normal (ULN) or serum
                  creatinine clearance (CrCl) ≥ 40 ml/min

               -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x ULN (≤
                  5 x ULN for patients with documented liver metastases)

               -  Alkaline phosphatase ≤ 2 X ULN (≤ 5 X ULN for those with bone metastasis)

               -  Total bilirubin ≤ 1.5 X ULN except those with direct bilirubin or Gilbert's
                  syndrome

               -  Serum lactate dehydrogenase (LDH) ≤ 10 X ULN

        Exclusion Criteria:

          -  Allergy to rituximab, or any of the ingredients in rituximab injection or rituximab
             and hyaluronidase human injection.

          -  Patients with active central nervous system (CNS) metastatic disease or leptomeningeal
             disease. Patients with CNS metastatic disease that has been treated with surgical
             resection or stereotactic radiosurgery are eligible if lesions are stable for at least
             4 weeks following therapy as determined by magnetic resonance imaging (MRI) scan done
             within one week of randomization.

          -  Prior therapy with immune checkpoint blocking antibodies (unless monotherapy given at
             least 1 year prior to starting combination therapy and no grade 3-4 toxicities while
             on monotherapy), vaccines or interleukin-2 (IL-2).

          -  Patients may have had prior systemic therapy in the adjuvant setting (e.g. interferon,
             proto-oncogene B-Raf [BRAF], or mitogen-activated protein-extracellular
             signal-regulated kinase [MEK] agents). Adjuvant ipilimumab, nivolumab, or
             pembrolizumab as single agent is allowed if greater than 1 year since last treatment
             and patient had no grade 3 or 4 toxicities from the checkpoint inhibitors.

          -  Women must not be pregnant or lactating. Must have negative urine or blood pregnancy
             test within 1 week of starting therapy.

          -  Patients with known human immunodeficiency virus (HIV) are ineligible.

          -  Patients with active Hepatitis B Virus (HBV) or Hepatitis C virus (HCV) are
             ineligible. -- ----Patients with prior history of, or serology suggestive of prior
             infection with Hepatitis B Virus (HBV) or Hepatitis C virus (HCV) are also ineligible.

          -  Patients with active, known or suspected autoimmune disorders including lupus and type
             I diabetes are ineligible. Patients with history of vitiligo, thyroiditis are
             eligible.

          -  Patients with active disease or history of inflammatory bowel disease are ineligible.

          -  Patients cannot be on corticosteroid therapy except as physiologic replacement
             therapy.

          -  Patients receiving ongoing corticosteroid therapy for autoimmune disorders are
             ineligible. Occasional steroid inhaler use or nasal spray are allowed. Patients
             receiving replacement doses of steroids for adrenal insufficiency are eligible.

          -  Patients must not have any serious underlying medical conditions or take medications
             that in the investigators opinion may interfere with compliance or interpretation of
             Immune-related adverse events (IRAEs).