Carboplatin, Paclitaxel, and Bevacizumab With or Without Everolimus in Treating Patients With Metastatic Malignant Melanoma

Inclusion Criteria: * Histologic proof of stage IV malignant melanoma not amenable to surgery; (biopsy can be of locoregional disease in setting of clinically evident stage IV disease, but primary tumor alone will not qualify) * At most one prior chemotherapy based regimen for metastatic melanoma (no prior taxane-based regimens allowed); note: prior adjuvant non-taxane based chemotherapy and/or adjuvant immunotherapy are allowed; no limit on the number of prior biologic, immunologic or targeted therapies * Measurable disease defined as at least one lesion whose longest diameter can be accurately measured as \>= 2.0 cm with chest x-ray, or as \>= 1.0 cm with computed tomography (CT) scan, CT component of a positron emission tomography (PET)/CT, or magnetic resonance imaging (MRI) scan; note: disease that is measurable by physical examination only is not eligible * Life expectancy \>= 4 months * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Absolute neutrophil count (ANC) \>= 1500/mL * Platelets (PLT) \>= 100,000 x 10\^9/L * Hemoglobin (Hgb) \>= 9 g/dL (patients may be transfused to meet this requirement) * Total cholesterol =\< 300 mg/dL and; (note: serum levels of cholesterol or triglycerides found to be elevated may be lowered with anti-lipid therapy, but must be documented to be below these levels prior to enrollment) * Triglycerides =\< 2.5 X upper limit of normal (ULN); (note: serum levels of cholesterol or triglycerides found to be elevated may be lowered with anti-lipid therapy, but must be documented to be below these levels prior to enrollment) * Creatinine =\< 1.5 x ULN * Total bilirubin =\< 1.5 mg/dL (exception: patients with documented Gilbert's syndrome are allowed to participate despite elevated bilirubin) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x ULN * Urine protein:creatinine (UPC) ratio \< 1.0 at screening OR * Urine dipstick for proteinuria \< 2+ (patients discovered to have \>= 2+ proteinuria on dipstick urinalysis at baseline should undergo a 24 hour urine collection and must demonstrate =\< 1 g of protein in 24 hours to be eligible) * Negative pregnancy test done =\< 7 days prior to registration/randomization, for women of childbearing potential only * Ability to understand and the willingness to sign a written informed consent document * Willing to return to a North Central Cancer Treatment Group (NCCTG) institution for follow-up * Willing to provide mandatory blood samples for research purposes * Willing to follow a diet low in fat and cholesterol while taking everolimus * Willing to abstain from eating grapefruit or drinking grapefruit juice for the duration of the study Exclusion Criteria * Prior treatment with agents disrupting vascular endothelial growth factor (VEGF) activity (i.e., bevacizumab, VEGF-trap, anti-VEGF receptor \[R\] monoclonal antibody \[Mab\]) or targeting VEGFR (e.g. sunitinib, sorafenib) * Prior treatment with an mTOR inhibitor for melanoma (sirolimus, temsirolimus, everolimus) * Brain metastases per MRI or CT at any time prior to registration; note: patients that have had primary therapy for brain metastasis (i.e. surgical resection, whole brain radiation, or stereotactic radiation therapy \[SRT\] even if stable) are not eligible * Other investigational agents =\< 4 weeks prior to registration/randomization * Chemotherapy treatment =\< 3 weeks prior to registration/randomization * Any biologic, immunologic or targeted therapy =\< 2 weeks prior to registration/randomization * Major surgical procedure, open biopsy, or significant traumatic injury =\< 4 weeks prior to registration/randomization * Fine needle aspirations or core biopsies =\< 7 days prior to registration/randomization * Planned/or anticipated major surgical procedure during the course of the study * Other medical conditions including but not limited to: * History of liver disease such as cirrhosis, chronic active hepatitis, chronic persistent hepatitis or hepatitis B or C * Active infection requiring parenteral antibiotics * Poorly controlled high blood pressure (\>=150 mm Hg systolic and/or 100 mmHg diastolic) despite treatment * New York Heart Association class II-IV congestive heart failure * Serious cardiac arrhythmia requiring medication * Myocardial infarction or unstable angina =\< 6 months prior to registration/randomization * Clinically significant peripheral vascular disease * Deep venous thrombosis or pulmonary embolus =\< 1 year of registration/randomization and/or ongoing need for full-dose oral or parenteral anticoagulation * Ongoing anti-platelet treatment other than low-dose aspirin (i.e., aspirin 81 mg orally \[p.o.\] daily) * Active bleeding or pathological conditions that carry high risk of bleeding (e.g., known esophageal varices, etc.) * Serious, non-healing wound (including wounds healing by secondary intention), ulcer or bone fracture * History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess =\< 6 months prior to registration/randomization * History of central nervous system (CNS) disease (e.g., primary brain tumor, vascular abnormalities, etc.), clinically significant stroke or transient ischemic attack (TIA) =\< 6 months prior to registration/randomization, seizures not controlled with standard medical therapy * Radiographically documented tumor invading major blood vessels * History of hypertensive crisis or hypertensive encephalopathy * Uncontrolled diabetes as defined by fasting serum glucose \> 1.5 x ULN * Severely impaired lung function as defined as spirometry and diffusing capacity of the lung for carbon monoxide (DLCO) that is 50% of the normal predicted value and/or 02 saturation that is 88% or less at rest on room air * A known history of human immunodeficiency virus (HIV) seropositivity * Any of the following as this regimen may be harmful to a developing fetus or nursing child: * Pregnant women * Nursing women * Men and women of reproductive potential who are not using effective birth control methods must use highly effective contraception throughout the trail and for 6 months after last study treatment * Existence of peripheral sensory neuropathy \>= grade 2 * History of other malignancy =\< 5 years with the exception of basal cell or squamous cell carcinoma of the skin, treated with local resection only, or carcinoma in situ (e.g. of the cervix, breast, prostate, etc.) * =\< 4 weeks since last day of adjuvant radiation therapy prior to registration or =\< 2 weeks since last day of palliative radiation therapy; NOTE: patients who have had \> 25% of their functional bone marrow irradiated are not eligible for this trial * Active or recent history of hemoptysis (\>= 1/2 teaspoon of bright red blood per episode) =\< 30 days prior to registration * Known hypersensitivity to any of the components of the everolimus, bevacizumab, carboplatin, or paclitaxel * Current use of drugs that are known to be strong inhibitors or inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4); note: if these agents are discontinued, everolimus therapy can begin \>= 7 days after discontinuation of such agent * Positive hepatitis B antigen (HBsAg) or hepatitis C serology (HCV) tests * Planned immunization with attenuated live vaccines =\< 7 days prior to registration or during study period; note: close contact with those who have received attenuated live vaccines should be avoided during treatment with everolimus; examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacillus Calmette-Guérin (BCG), yellow fever, varicella and TY21a typhoid vaccines