Inclusion Criteria:

          -  Advanced or unresectable melanoma of presumed uveal origin. Non-uveal melanomas with
             "malignant blue nevus" physiology with GNAQ, GNA11, CYSLTR2, or PLCB4 driver
             alterations are eligible upon discussion with the Principal Investigator.

          -  Disease must be measurable according to RECIST 1.1. Disease that has undergone local
             therapy in the past 30 days is not considered measurable unless the investigator has
             documented progression despite the local therapy.

          -  Disease must be amenable to a biopsy attempt, in the opinion of the investigator.

          -  Asymptomatic untreated brain metastases are allowed. Symptomatic brain metastases that
             have undergone local therapy with RT or surgery and have not required an increase in
             steroid dose in prior 2 weeks are allowed.

        Note: Seizure prophylaxis with untreated brain metastases are allowed.

          -  Patients must have an Easter Cooperative Oncology Group (ECOG) Performance Statue (PS)
             of 0-1.

          -  Acceptable liver, renal, and hematological function:

          -  Total bilirubin </= 1.5x upper limit of normal (ULN); patients with Gilbert's Syndrome
             must have bilirubin </= 3x ULN

          -  Aspartate aminotransferase (AST/SGOT) and alanine aminotransferase (ALT/SGPT) </= 3 x
             ULN (</= 5x if liver metastases are present)

          -  Estimated glomerular filtration rate (GFR) >/= 30 mL/min using a cancer-specific GFR
             Model; the calculator found at:

        http://tavarelab.cruk.com.ac.uk/JanowitzWilliamsGFR/

          -  Hemoglobin >/= 9 g/dL

          -  Neutrophils >/= 1.5 x 10^9/L

          -  Platelets >/= 100 x 10^9/L

          -  Female patients of childbearing potential and their partners (if male) and male
             patients with female partners of childbearing potential and their partners must agree
             to use a highly effective form of contraception for the duration of the study from the
             list below or agree to refrain from intercourse for the duration of the trial and for
             at least 30 days after the last administration of ADI-PEG20 and at least 150 days (if
             female) or 210 days (if male) after the final dose of ipilimumab and/or nivolumab
             whichever is later. Highly effective forms of contraception include the following:

               -  combined (estrogen and progestogen containing) hormonal contraception associated
                  with inhibition of ovulation (oral, intravaginal or transdermal)

               -  progestogen-only hormonal contraception associated with inhibition of ovulation
                  (oral, injectable, implantable)

               -  intrauterine device

               -  intrauterine hormone-releasing system

               -  bilateral tubal occlusion

               -  vasectomized partner

        Exclusion Criteria:

          -  Other active malignancy that in the opinion of the treating investigator will
             interfere with the assessments of efficacy for uveal melanoma in this study

          -  History of seizure disorder not related to malignancy

          -  Pregnancy or lactation

          -  Expected non-adherence to protocol

          -  Known allergy to E. coli drug products (such as GM-CSF)

          -  Known allergy to pegylated compounds

          -  Prior treatment with ADI-PEG20 or another experimental arginine deprivation strategy

          -  Systemic anticancer therapy within 3 weeks or 1 cycle length, whichever is shorter, of
             first day of planned study therapy

          -  Presence of treatment-related adverse events that have not recovered or stabilized at
             Grade 1 (excepting vitiligo and alopecia or treated endocrine conditions). AEs that
             are Grade 2 that are not felt to be a significant safety risk (e.g. rash, asymptomatic
             thyroiditis) may be allowable upon discussion with the Principal Investigator.

          -  Active autoimmune disease or any condition requiring greater than 10mg prednisone per
             day equivalent or other immune suppressive medication (e.g. anti-TNF agents) within 14
             days of study screening. Inhaled or topical steroids and adrenal replacements does of
             steroids >10mg prednisone are allowed in the absence of active autoimmune disease.

          -  History of myocarditis or motor neuropathy of any grade

          -  Gout flares within the past 28 days or sequelae of chronic gout, such as gouty
             arthritis, are excluded.

        Note: Patients with asymptomatic hyperuricemia without arthralgias or arthritic symptoms
        are eligible, as are patients with known gout on chronic uric acid lowering medication who
        have not experienced a flare within 28 days