Trial of Vemurafenib/Cobimetinib With or Without Bevacizumab in Patients With Stage IV BRAFV600 Mutant Melanoma

Inclusion Criteria: 1. Patients must have histological or cytological confirmed melanoma that is metastatic or unresectable stage IIIc and clearly progressive. 2. Patients must have melanoma that is documented to contain a BRAFV600E or BRAFV600K mutation by a FDA-approved test. 3. Age \>= 18 years. 4. Women must not be pregnant due to the fact that the effects of vemurafenib, cobimetinib, and/or bevacizumab on the developing human fetus are unknown. For this reason and because antiangiogenic agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence; defined in Appendix G) prior to study entry and for the duration of study participation. Should a woman become pregnant while participating in this study, she should inform her treating physician immediately. 5. All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy. A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). 6. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with bevacizumab, cobimetinib, and vemurafenib, female participants who are breastfeeding must agree to discontinue nursing prior to Day 1 of the study. 7. Patients must have measurable disease as defined in Section 10.1 (cutaneous lesions measuring at least 1 cm will be considered measurable). Baseline CT or MRI scans of measurable disease sites must be performed within 4 weeks of study entry. 8. Patients must have discontinued immunotherapy or other systemic therapy including investigational agents at least 4 weeks prior to entering the study and have recovered from adverse events due to those agents. Patients must agree to not receive any other investigational agents during study participation. 9. Patients must have an ECOG performance status of 0, 1, or 2. 10. Patients must have the following baseline laboratory values: 1. White Blood Count \> 3,000/mm3 2. Absolute Neutrophil Count \> 1,500/mm3 3. Platelet Count \> 100,000/mm3 4. Serum creatinine \< 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl)\> 40ml/min (CrCl= Wt (kg) x (140-age)\*/72 x Cr. level, \*female x 0.85) 5. Aspartate aminotransferase (AST) / alanine aminotransferase (ALT) \< 3 x ULN (\< 5 x ULN for patients with documented liver metastases) 6. Alkaline Phosphatase =\< 2 x ULN (=\< 5 x ULN for patients with known liver involvement and =\< 7 x ULN for patients with known bone involvement) 7. International Normalized Ratio (INR) \< 1.5 and aPTT within 1.1 x ULN 8. Total Bilirubin \< 1.5 x ULN 9. UPC ratio \< 1.0 at screening or 24 hours urine protein \< 1 gm (Appendix D) 11. Patients must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 1. Patients may not have received more than 2 prior systemic treatment regimens for distant metastatic disease. The following prior therapy is permitted in either the adjuvant or metastatic disease setting, provided treatment is discontinued at least 4 weeks prior to initiating study treatment: 1. Immunotherapy, such as interferon, interleukin-2, GM-CSF, ipilimumab, anti-PD1 or other experimental agent. 2. Cytotoxic chemotherapy, such as dacarbazine, temozolomide, carboplatin +/-paclitaxel. 2. Patients may not have had radiation therapy within the last 4 weeks prior to initiation of study treatment. 3. Patients who have had prior VEGF pathway inhibitor, BRAF or MEK inhibitor therapy are ineligible. 4. Patients must have no clinical evidence of active brain metastasis. Patients with a history of brain metastases must meet all of the following criteria: 1. Have completed treatment greater than 4 weeks prior to enrollment. 2. Have CNS lesions that are confirmed to be stable or regressing on imaging since the time of the last CNS treatment including the pre-treatment CT or MRI scan for this trial. 3. Patients must have no residual neurologic symptoms while taking no steroids, a stable or decreasing dose of steroids, or a stable dose of anti-seizure medication for the 2 weeks prior to enrollment. 5. Patients must not have other concurrent uncontrolled malignancies, defined as a malignancy that currently requires therapy or other intervention. Patients with suspected cuSCCs should have them excised prior to study registration. Surgical resection should not be performed within 7 days of starting protocol therapy. 6. Patients may not have had a major surgical procedure, open biopsy (excluding skin cancer resection, cutaneous/subcutaneous melanoma metastasis resection or biopsy or vascular access device insertion), or significant traumatic injury within 28 days prior to Day 1, or have an anticipated need for major surgical procedure or a planned elective surgical procedure during the course of the study. 7. Patients may not have had a core biopsy, skin cancer resection, or other minor surgical procedure, including placement of a vascular access device, within 7 days prior to Day 1 of the protocol. 8. Patients must not have a serious intercurrent illness including, but not limited to: 1. Ongoing or active infection requiring parental antibiotics on Day 1 2. A history of malabsorption or other condition that would interfere with absorption of vemurafenib or cobimetinib. 3. History of hemoptysis (\>= 1/2 teaspoon of bright red blood per episode) within 1 month prior to Day 1 4. History of congenital long QT syndrome or mean corrected QTc interval \> 450 msec at baseline 5. Clinically significant cardiovascular disease, defined as any of the following conditions: i. Uncontrolled hypertension (defined as systolic blood pressure \> 150 mmHg and/or diastolic blood pressure \> 100 mmHg) ii. Prior history of hypertensive crisis or hypertensive encephalopathy iii. Myocardial infarction within 6 months iv. Unstable angina v. New York heart association grade II or greater congestive heart failure (Appendix C) vi. Serious cardiac arrhythmia requiring medication vii. LVEF \< 50% or below institutional limit of normal f) History of stroke of TIAs within 6 months prior to Day 1 g) Grade II or greater peripheral vascular disease within 1 year prior to study entry or other significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to Day 1 h) Serious, non-healing wound, active ulcer, or untreated bone fracture i) History of abdominal fistula or gastrointestinal perforation within 6 months prior to Day 1 j) Known hypersensitivity to any component of bevacizumab k) Known CNS disease, except for stable or regressing brain metastases. l) Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) m) Psychiatric illness/social situations that would limit compliance with study requirements. n) Significant ocular issues including history of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment, retinal vein occlusion (RVO), or neovascular macular degeneration. The risk factors for RVO are listed below. Patients should be excluded if they have the following conditions: 1. Uncontrolled glaucoma with intra-ocular pressures \>21mm Hg 2. Serum cholesterol \>= Grade 2 3. Hypertriglyceridemia \>= Grade 2 4. Hyperglycemia (fasting) \>= Grade 2 9. Patients must not have the following foods/ supplements at least 7 days prior to initiation of and during study treatment: 1. St. John's wort or hyperforin (potent cytochrome P450 CYP3A4 enzyme inducer) 2. Grapefruit juice (potent cytochrome P450 CYP3A4 enzyme inhibitor). 10. Because patients with immune deficiency are at increased risk of lethal infections when treated with bone marrow-suppressive therapy, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with bevacizumab, vemurafenib and cobimetinib.