Sorafenib, Carboplatin, and Paclitaxel in Treating Patients With Stage IV Melanoma of the Eye

Criteria: * Histologically proven uveal melanoma * Must have documented disease progression during or after =\< 1 prior systemic treatment * Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques or \>= 10 mm by spiral CT scan * No tumor involving major vessels * Zubrod performance status 0-1 * Absolute neutrophil count \> 1,500/mm\^3 * Platelet count \> 100,000/mm\^3 * Creatinine =\< 2 times upper limit of normal (ULN) * Bilirubin =\< 2 times ULN * SGOT or SGPT =\< 2 times ULN (5 times ULN if hepatic metastasis present) * INR in range (usually between 2 and 3) * No active bleeding * No bleeding diathesis, active coagulopathy, or pathological condition that carries a high risk of bleeding * No condition (e.g., gastrointestinal tract disease) affecting ability to take oral medication or requiring IV alimentation * Not pregnant or nursing * Fertile patients must use effective contraception * No prior malignancy except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer for which the patient is currently in complete remission, or any other cancer for which the patient has been disease-free for 5 years * At least 28 days since prior systemic treatment for this disease comprising 1 of the following: single chemotherapy agent/regimen; single immunotherapy agent/regimen; single investigational treatment agent/regimen * At least 21 days since prior major surgery * No prior sorafenib or any other agents targeting raf kinase or vascular endothelial growth factor (VEGF) or VEGF receptor * No prior surgical procedures affecting absorption * No concurrent systemic corticosteroid therapy * Topical and/or inhaled steroids are allowed * No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (e.g., phenytoin, carbamazepine, and phenobarbital), rifampin, or Hypericum perforatum (St. John's wort) * No prophylactic granulocyte/platelet colony-stimulating factors during the first course of treatment * Concurrent full-dose oral anticoagulants (e.g., warfarin) are allowed provided all of the following criteria are met: in-range INR ; stable dose of oral anticoagulant; no active bleeding or high risk of bleeding * Stage IV disease * No known varices * No uncontrolled hypertension with systolic blood pressure (BP) \> 140 mm Hg or diastolic BP \> 90 mm Hg * No significant traumatic injury within the past 21 days * No active, uncontrolled peptic ulcer disease