The goal of this clinical research study is to find out if Cemiplimab plus Ziv-Aflibercept is safe and effective in treating your condition of metastatic (spread to other parts of your body) uveal melanoma. This research study will test the study drugs to see if the combination of Cemiplimab plus Ziv-Aflibercept can make tumors shrink or stop growing.

Inclusion Criteria:

• Provision of signed and dated informed consent form.

• Male or female, aged >/= 18 years old.

• Life expectancy of greater than 3 months in the opinion of the investigator.

• Must be willing and able to provide informed consent signed by study patient or legally acceptable representative, as specified by health authorities and institutional guidelines.

• Patients must have metastatic uveal melanoma, either initial presentation or recurrent, that is histologically diagnosed.

• Patients with histologically or cytologically confirmed metastatic melanoma or cutaneous, mucosal or unknown primary origin are also eligible. This includes AJCC stage IV or advanced/inoperable stage III. This also includes patients with a history of lower stage melanoma and subsequent recurrent metastatic disease that is either locally/regionally advanced/inoperable disease or distant metastases. These patients must have previously received anti-PD1 immunotherapy (nivolumab or pembrolizumab) as monotherapy or in combination and later experienced disease progression. Patients with BRAF V600 mutant melanoma must have previously received BRAF targeted therapy for metastatic melanoma and later experienced disease progression. Patients who refuse or decline to receive BRAF targeted therapy or prefer to delay or were intolerant of BRAF targeted therapy are eligible

• Patients must have ECOG performance status of 0-1.

• Patients must have measurable disease, according to RECIST version 1.1.

• Patients must have normal organ and marrow function as defined in protocol.

• Urine protein should be screened by urinalysis for Urine Protein Creatinine Ratio (UPCR). For UPCR > 1, a 24-hour urine protein should be obtained, and the level should be <500 mg.

• An echocardiogram should be performed at baseline in all patients. Ejection fraction (EF) from baseline echocardiogram must be within the institutional limits of normal as determined by the reading cardiologist.

• Patients on full-dose anticoagulants (e.g., warfarin) with PT INR >1.5 are eligible provided that both of the following criteria are met:

  1. The patient has an in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin.
  2. The patient has no active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices).

• A patient may be treatment naïve. However, prior systemic treatments for metastatic uveal melanoma are allowed. There is no limit on the number of prior regimens for metastatic uveal melanoma. However, no prior therapy with bevacizumab, aflibercept or cemiplimab.

• Patients must be free of active brain metastasis by contrast-enhanced CT/MRI scans within 4 weeks prior to enrollment. If known to have prior brain metastases, these must have been adequately managed with standard of care radiation therapy, stereotactic radiosurgery or surgery prior to registration on the study.

• For Women of childbearing potential: use of highly effective contraception for at least 2 or more menstrual cycles prior to screening and agreement to use such a method during study participation and for at least 180 days after the end of study drugs administration.

• For males of reproductive potential: use of condoms or other methods to ensure effective contraception with partner For at least 1 month prior to screening and agreement to use such a method during study participation and for at least 180 days after the end of study drugs administration.

Exclusion Criteria:

• Pregnancy or lactation.
• Treatment with another investigational drug or other systemic intervention for uveal melanoma within 4 weeks of initiation of study drugs. Patients must not have radiotherapy within the preceding 4 weeks.

Patients must have recovered from adverse events due to agents administered more than 4 weeks earlier.

• Patients must be at least 4 weeks from major surgery and have fully recovered from any effects of surgery and be free of significant detectable infection.
• Patients must not have autoimmune disorders or conditions of immunosuppression that require current ongoing treatment with systemic corticosteroids (or other systemic immunosuppressants), including oral steroids (i.e., prednisone, dexamethasone) or continuous use of topical steroid creams or ointments or ophthalmologic steroids. A history of occasional (but not continuous) use of steroid inhalers is allowed.

Replacement doses of steroids for patients with adrenal insufficiency are allowed. Patients who discontinue use of these classes of medication for at least 2 weeks prior to enrollment are eligible if, in the judgment of the treating physician investigator, the patient is not likely to require resumption of treatment with these classes of drugs during the study.

• Exclusion from this study also includes patients with a history of symptomatic autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis [scleroderma], systemic lupus erythematosus, Sjögren's syndrome, autoimmune vasculitis [e.g., Wegener's granulomatosis]); motor neuropathy considered of autoimmune origin (e.g., Guillain-Barre Syndrome and Myasthenia Gravis); other central nervous system autoimmune disease (e.g., poliomyelitis, Multiple sclerosis).

• Immunosuppressive corticosteroid doses (>10 mg prednisone daily or equivalent) within 4 weeks prior to the first dose of cemiplimab/placebo. NOTE: Patients who require brief course of steroids (eg, prophylaxis for imaging assessments due to hypersensitivity to contrast agents) are not excluded. People taking steroids for physiologic replacement (ie, adrenal insufficiency) are NOT excluded.

• Prior allogeneic stem cell transplantation, or autologous stem cell transplantation.

• Patients who have permanently discontinued anti-cancer immune modulating therapies due to drug related toxicity.

• Encephalitis, meningitis, or uncontrolled seizures in the year prior to screening/enrollment.

• History of immune related pneumonitis within the last 5 years.

• History of interstitial lung disease (eg, idiopathic pulmonary fibrosis, organizing pneumonia) or active, noninfectious pneumonitis that required immune-suppressive doses of glucocorticoids to assist with management. A history of radiation pneumonitis in the radiation field is permitted as long as pneumonitis resolved ≥6 months prior to the enrollment date.

• Patients with a history of solid organ transplant (patients with prior corneal transplant(s) are not excluded).

• Patients with autoimmune hypothyroid disease or type I diabetes on replacement treatment are eligible.

• Patients must not have a history of inflammatory bowel disease or diverticulitis (history of diverticulosis is allowed).

• Patients must not have other significant medical, surgical, or psychiatric conditions or require any medication or treatment that in the opinion of the investigator may interfere with compliance, make the administration of cemiplimab hazardous or obscure the interpretation of AEs, such as a condition associated with frequent diarrhea.

• Patients must not have an active infection requiring current treatment with parenteral antibiotics.

• Cardiac: No evidence of congestive heart failure, symptoms of coronary artery disease, myocardial infarction less than 6 months prior to entry, serious cardiac arrhythmias, or unstable angina.

• Central nervous system: No history of cerebrovascular accident or transient ischemic attacks within the past 6 months.

• Serious or non-healing wound, ulcer, or bone fracture.

• History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 4 weeks of initiating study treatment.

• Patients with the following invasive procedures:

  • Major surgical procedure, open biopsy or significant traumatic injury within 4 weeks of Day 1 of study therapy.
  • Anticipation of need for major surgical procedures during the course of the study.
  • Minor surgical procedures, fine needle aspirations or core biopsies within 7 days prior to Day 1 of study therapy. Central venous catheter placements are permitted to be completed 7 or more days prior to Day 1 of study therapy. However, peripherally inserted central catheter (PICC or PIC line) may be placed at any time prior to or during study therapy.

• Patients with clinically significant cardiovascular or cerebrovascular disease:

  • History of cerebrovascular accident or transient ischemic attack within past 6 months
  • Uncontrolled hypertension, defined as blood pressure >150/100 mm Hg or systolic BP >180 mm Hg if diastolic blood pressure <90 mm Hg, on at least 2 repeated determinations on separate days within past 3 months.
  • Myocardial infarction, coronary artery bypass grafting (CABG) or unstable angina within the past 6 Months.
  • New York Heart Association grade III or greater congestive heart failure, serious cardiac arrhythmia requiring medication, unstable angina pectoris within past 6 months.
  • Clinically significant peripheral vascular disease within past 6 months.
  • Pulmonary embolism, deep vein thrombosis (DVT), or other thromboembolic event within past 6 months.

• History of tumor-related or other serious hemorrhage, bleeding diathesis, or underlying coagulopathy.

• PT INR >1.5 unless the patient is on full-dose warfarin.

• Patients who have other current malignancies are not eligible. Patients with other malignancies are eligible if they have been continuously disease free for > 3 years prior to the time of enrollment. Patients with prior history at any time of any in situ cancer, lobular carcinoma of the breast in situ, cervical cancer in situ, atypical melanocytic hyperplasia or melanoma in situ are eligible. Patients with prior history of basal or squamous skin cancer are eligible. Patients who have had multiple primary melanomas are eligible.

• Receipt of a live vaccine within 28 days of the enrollment date.

• Women of childbearing potential or sexually active men, who are unwilling to practice highly effective contraception for at least 2 or more menstrual cycles (women) or 1 month (men) prior to screening, during the study, and for at least 180 days after the last dose of study drug(s).