Bevacizumab and Atezolizumab With or Without Cobimetinib in Treating Patients With Untreated Melanoma Brain Metastases

Inclusion Criteria: * Signed informed consent form (ICF) * Age \>/= 18 years * Ability and willingness to comply with the requirements of the study protocol * Life expectancy \> 12 weeks * Asymptomatic off steroids for at least 10 days except patients: a) who have mild symptoms from intracranial disease that do not affect their performance status; or b) who are asymptomatic, but require steroids for control of symptoms on a maximum dose of dexamethasone 4mg/day orally (PO) or equivalent * Prior therapies for extracranial metastatic melanoma including chemotherapy, BRAFi/MEKi, cytokine or vaccine therapy as long as it did not include PD-1/PD-L1. Note: Patients who are PD-1 refractory are allowed to enroll into the TACo arm if BRAFV600 wild-type is confirmed. Patients that are known to have BRAFV600 mutation must have received prior BRAFi/MEKi prior to enrolling on TACo. Patients that have received prior BRAF/MEKi have to have received their last dose of BRAF/MEKi \> 3 months prior to being treated on this study. * At least one measurable intracranial target lesion for which all of the following criteria are met: a) Previously untreated or progressive after previous local therapy b) Immediate local therapy clinically not indicated or patient is not a suitable candidate to receive immediate local therapy c) Largest diameter of \>= 0.5 cm, but =\< 3 cm as determined by contrast-enhanced MRI * Representative formalin-fixed paraffin-embedded (FFPE) tumor specimens in paraffin blocks (blocks are preferred) or at least 4 unstained slides, with an associated pathology report, for central testing of tumor PD-L1 expression a) Tumor tissue should be of good quality based on total and viable tumor content. Fine needle aspiration, brushing, cell pellet from pleural effusion, bone metastases, and lavage samples are not acceptable. For core-needle biopsy specimens, at least three cores should be submitted for evaluation. b) Patients who do not have tissue specimens meeting eligibility requirements may undergo a biopsy during the screening period. Acceptable samples include core needle biopsies for deep tumor tissue (minimum of three cores) or excisional, incisional, punch, or forceps biopsies for cutaneous, subcutaneous, or mucosal lesions. c) Tumor tissue from bone metastases is not evaluable for PD-L1 expression and is therefore not acceptable * Histologically or cytologically confirmed BRAFV600 wild-type melanoma through archival or newly obtained tissue.(only patients who are PD-1 refractory who will enroll onto the TACo arm) * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Absolute neutrophil count (ANC) \>= 1500 cells/u * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): White blood cell (WBC) counts \> 2500/uL * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Lymphocyte count \>= 500/uL * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Platelet count \>= 100,000/uL * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Hemoglobin \>= 9.0 g/dL * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Total bilirubin =\< 1.5 x upper limit of normal (ULN) with the following exception: 1) patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN with the following exception: 1) patients with documented liver metastases: AST and/or ALT =\< 5 x ULN * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Alkaline phosphatase =\< 2.5 x ULN with the following exception: 1) =\< 5 x ULN in patients with documented liver metastases =\< 7 x ULN in patients with documented bone metastases * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Serum creatinine =\< 1.5 x ULN or creatinine clearance \>= 50 mL/min on the basis of the Cockcroft-Gault glomerular filtration rate estimation * Obtained within 14 days prior to the first study treatment (cycle 1, day 1): Urine dipstick for proteinuria \< 2+ unless a 24-hour urine protein =\< 1 g of protein is demonstrated * For female patients of childbearing potential and male patients with partners of childbearing potential, agreement (by patient and/or partner) to use highly effective form(s) of contraception (i.e., one that results in a low failure rate \[\< 1% per year\] when used consistently and correctly) and to continue its use for at least 12 months after the last dose of atezolizumab * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN within 7 days prior to study enrollment Exclusion Criteria: * Symptomatic brain metastases requiring immediate local interventions such as craniotomy or stereotactic radiosurgery (SRS) * Patients who require immediate surgical or radiotherapy interventions * Increasing corticosteroid dose in 7 days prior to administration of first dose of study drug. Symptomatic patients who have stable or decreasing corticosteroid use in the past 7 days may be included * Patients with leptomeningeal disease * Any approved anticancer therapy, including chemotherapy and hormonal therapy within 3 weeks prior to initiation of study treatment; however, the following are allowed: a) Hormone-replacement therapy or oral contraceptives b) Herbal therapy \> 1 week prior to cycle 1, day 1 (herbal therapy intended as anticancer therapy must be discontinued at least 1 week prior to cycle 1, day 1) * Current, recent (within 3 weeks of the first infusion of this study), or planned participation in an experimental drug study other than a Genentech-sponsored bevacizumab cancer study * Adverse events (AEs) from prior anticancer therapy that have not resolved to grade =\< 1 except for alopecia * Bisphosphonate therapy for symptomatic hypercalcemia a) Use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease. Patients with acute leukemias, accelerated/blast phase chronic myelogenous leukemia, chronic lymphocytic leukemia, Burkitt lymphoma, plasma cell leukemia, or non-secretory myeloma * Patients who are pregnant, lactating, or breastfeeding * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * Inability to undergo MRI secondary to: a) metal b) claustrophobia c) gadolinium contrast allergy * Prior radiation therapy within the last 14 days * Inability to comply with study and follow-up procedures * History of autoimmune disease, including but not limited to systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis a) Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible. b) Patients with controlled Type 1 diabetes mellitus on a stable insulin regimen may be eligible. c) Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions: Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations; rash must cover less than 10% of body surface area (BSA) * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%) No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) * History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan a) history of radiation pneumonitis in the radiation field (fibrosis) is permitted * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications * History of human immunodeficiency virus (HIV) infection or active hepatitis B (chronic or acute) or hepatitis C infection; a) Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible; b) Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * Active tuberculosis * Severe infections within 4 weeks prior to cycle 1, day 1, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia * Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1 * Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study a) Influenza vaccination should be given during influenza season only (approximately October to March). Patients must not receive live, attenuated influenza vaccine (e.g., FluMist) within 4 weeks prior to cycle 1, day 1 or at any time during the study * Malignancies other than the disease under study within 5 years prior to cycle 1, day 1, with the exception of those with a negligible risk of metastasis or death and with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, or ductal carcinoma in situ treated surgically with curative intent) or undergoing active surveillance per standard-of-care management (e.g., chronic lymphocytic leukemia Rai Stage 0, prostate cancer with Gleason score =\< 6, and prostate-specific antigen \[PSA\] =\< 10 mg/mL, etc.) * Known hypersensitivity to any component of bevacizumab, atezolizumab, or cobimetinib * Life expectancy of less than 12 weeks * (Atezolizumab-related exclusion) Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway targeting agents a) Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met: Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose. No history of severe immune-related adverse effects from anti-CTLA 4 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] Grade 3 and 4) Patients who are PD-1 refractory are allowed to enroll into the TACo arm regardless of BRAF status. * (Atezolizumab-related exclusion) Treatment with systemic immunostimulatory agents (including but not limited to interferon \[IFN\]-(alpha) or interleukin \[IL\]-2) within 6 weeks or five half-lives of the drug (whichever is shorter) prior to cycle 1, day 1 * (Atezolizumab-related exclusion) Treatment with investigational agent within 4 weeks prior to cycle 1, day 1 (or within five half lives of the investigational product, whichever is longer) * (Atezolizumab-Related Exclusion) Treatment with systemic immunosuppressive medications (including but not limited to prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1 a) Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled. b) The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed * (Atezolizumab-related exclusion) History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * (Atezolizumab-related exclusion) Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation * (Bevacizumab-related exclusion) Inadequately controlled hypertension (defined as systolic blood pressure \> 150 mmHg and/or diastolic blood pressure \> 100 mmHg) * (Bevacizumab-related exclusion) Prior history of hypertensive crisis or hypertensive encephalopathy * (Bevacizumab-related exclusion) Clinically significant (i.e. active) cardiovascular disease, for example cerebrovascular accidents =\< 6 months prior to study enrolment, myocardial infarction =\< 6 months prior to study enrollment, unstable angina, grade II or greater congestive heart failure, or serious cardiac arrhythmia uncontrolled by medication or potentially interfering with protocol treatment * (Bevacizumab-related exclusion) History or evidence upon physical/neurological examination of central nervous system (CNS) disease (e.g. seizures) unrelated to cancer unless adequately treated with standard medical therapy * (Bevacizumab-related exclusion) Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior of study enrollment * (Bevacizumab-related exclusion) Any previous venous thromboembolism \> NCI CTCAE grade 3 * (Bevacizumab-related exclusion) History of hemoptysis (\>= 1/2 teaspoon of bright red blood per episode) within 1 month of study enrollment for any tumor type * (Bevacizumab-related exclusion) Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) * (Bevacizumab-related exclusion) Current or recent (within 10 days of study enrolment) use of aspirin (\> 325 mg/day), clopidogrel (\> 75 mg/day), or current or recent (within 10 days prior to first dose of bevacizumab) use of therapeutic oral or parenteral anticoagulants or thrombolytic agents for therapeutic purposes Note: The use of full-dose oral or parenteral anticoagulants is NOT permitted for at least two weeks at the time of study enrollment. Prophylactic use of anticoagulants is NOT allowed * (Bevacizumab-related exclusion) Surgical procedure (including open biopsy, surgical resection, wound revision, or any other major surgery involving entry into a body cavity) or significant traumatic injury within 28 days prior to study enrollment, or anticipation of need for major surgical procedure during the course of the study. For patients with brain tumours, craniotomy or intracranial biopsy sites must be adequately healed; free of drainage or cellulitis, and the underlying cranioplasty must appear intact at the time of study enrolment. * History of abdominal fistula or gastrointestinal perforation within 6 months prior to to the first study treatment Serious, non-healing wound, active ulcer, or untreated bone fracture (Adjuvant trials: bone fractures must be healed) * Proteinuria as demonstrated by a UPC ratio \>= 1.0 at screening Cobimetinib-Related Exclusion Criteria: * Inability to swallow medications * Malabsorption condition that would alter the absorption of rally administered medications * Ocular Melanoma * Left Ventricular Ejection Fraction (LVEF) is below the institutional lower limit of normal or \<50%, whichever is lower. * History or presence of an abnormal electrocardiogram (ECG) that is clinically significant in the investigator's opinion, including complete left bundle branch block, second- or third-degree heart block, or evidence of prior myocardial infarction. * Patients who meet any of the following exclusion criteria related to ocular disease will be excluded from study entry: * Known risk factors for ocular toxicity, consisting of any of the following: * History of serous retinopathy * History of retinal vein occlusion (RVO) * Evidence of ongoing serous retinopathy or RVO at screening