Bortezomib, Paclitaxel, and Carboplatin in Treating Patients With Metastatic Melanoma

Criteria:

* No uncontrolled intercurrent illness including any of the following: ongoing or active infection; symptomatic congestive heart failure; unstable angina pectoris; cardiac arrhythmia
* No psychiatric illness that would limit compliance with study requirements
* No other uncontrolled serious medical conditions (e.g., diabetes)
* No more than 1 prior cytotoxic chemotherapy regimen
* No more than 2 prior immunotherapy regimens either in adjuvant or metastatic setting
* At least 4 weeks since prior major radiotherapy or chemotherapy
* At least 8 weeks since prior monoclonal antibody therapy
* At least 4 weeks since prior immunotherapy or biologic therapy
* At least 3 weeks since prior surgery
* Recovered from prior therapies
* No prior therapy with bortezomib, paclitaxel, or carboplatin
* No other prior or concurrent chemotherapy, immunotherapy, radiotherapy, or any other therapy or supportive care considered investigational
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No concurrent prophylactic colony-stimulating factors
* Histologically confirmed malignant melanoma
* Patients with significant fluid retention, including ascites or pleural effusion, may be allowed at the discretion of the principal investigator
* No known brain metastases by brain imaging with contrast
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Routine urine analysis with predicted 24-hour urine protein \< 500 mg OR 1+ proteinuria by urine dipstick with 24-hour urine protein \< 500 mg
* Total bilirubin \< 1.5 mg/dL
* AST =\< 3 times ULN
* Creatinine =\< 1.5 times ULN
* ECOG performance status (PS) 0, 1, or 2 (Karnofsky PS \>= 60%)
* Life expectancy by physician estimate \> 12 weeks
* Not pregnant or nursing
* Fertile patients must use effective contraception during and for 6 months after completion of study treatment
* Negative pregnancy test
* No history of allergic reactions attributed to compounds of similar chemical or biologic composition to bortezomib
* No peripheral neuropathy \>= grade 2
* Manifestations of stage IV disease (e.g., cutaneous, uveal)
* All melanomas, regardless of origin, allowed
* Measurable disease, defined as at least one lesion whose longest diameter can be accurately measured as \>= 2.0 cm with conventional techniques or as \>= 1.0 cm with spiral CT scan
* No nonmeasurable disease only, including any of the following: bone lesions, leptomeningeal disease, ascites, pleural/pericardial effusion, inflammatory breast disease, lymphangitis cutis/pulmonis, abdominal masses that are not confirmed and followed by imaging techniques, cystic lesions
* Hemoglobin \>= 9.0 g/dL