Vemurafenib, Cobimetinib, Atezolizumab, and Tiragolumab in Treating Patients With High-Risk Stage III Melanoma

Inclusion Criteria: * PRE-REGISTRATION: Age \>= 18 years * PRE-REGISTRATION: High-risk stage III melanoma, defined as (any of the following): * Recurrent nodal metastasis, or * Clinically detectable nodal metastasis, or * Metastatic involvement of more than one nodal basin * NOTE: For the purpose of pre-registration, high-risk stage III melanoma is defined based on clinical and imaging assessment (positron emission tomography/computed tomography \[PET/CT\], CT, or magnetic resonance imaging \[MRI\]). Histologic confirmation of nodal metastatic disease is not needed at the time of pre-registration, provided there is histologic confirmation of primary melanoma or a prior lymph node metastasis. * PRE-REGISTRATION: Willing to submit archival tissue from a lymph node biopsy or undergo a needle biopsy (with clip placement) for BRAF testing and for research purposes. * PRE-REGISTRATION: Willing to forego anticancer treatments or investigational agents during pre-registration period. * PRE-REGISTRATION: The following laboratory values obtained =\< 28 days prior to pre-registration: * Only for patients receiving therapeutic anticoagulation: stable anticoagulant regimen and stable international normalized ratio (INR). * REGISTRATION: Histologic confirmation of stage III melanoma, as defined by the American Joint Committee on Cancer, 8th revised edition. * REGISTRATION: Arms A and B only: Documentation of BRAFV600 mutation status in melanoma tumor tissue (archival or newly obtained) through use of a Clinical Laboratory Improvement Amendments (CLIA)-approved clinical mutation test. * REGISTRATION: Surgically resectable disease, as determined by a melanoma surgical oncologist. * REGISTRATION: Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * REGISTRATION: Life expectancy \>= 26 weeks. * REGISTRATION: Absolute neutrophil count (ANC) \>= 1500/mm\^3 obtained =\< 14 days prior to registration. * REGISTRATION: Platelet count \>= 100,000/mm\^3 obtained =\< 14 days prior to registration. * REGISTRATION: Hemoglobin \>= 9.0 g/dL obtained =\< 14 days prior to registration. * REGISTRATION: Direct bilirubin =\< institutional upper limit of normal (ULN) obtained =\< 14 days prior to registration. * REGISTRATION: Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 2 x ULN obtained =\< 14 days prior to registration. * REGISTRATION: Alkaline phosphatase \< 2.5 x ULN obtained =\< 14 days prior to registration. * REGISTRATION: Creatinine =\< 1.5 x ULN or creatinine clearance (CrCl) \>= 45 mL/min on the basis of measured CrCl from a 24-hour urine collection or Cockcroft-Gault glomerular filtration rate estimation obtained =\< 14 days prior to registration. * REGISTRATION: Arms A and B only: Left ventricular ejection fraction (LVEF) \>= 50% or institutional lower limit of normal (LLN) =\< 6 months prior to registration. * REGISTRATION: Arms A and B only: Average corrected QT interval (QTc) =\< 450 ms on triplicate 12 lead electrocardiography (ECG) =\< 28 days prior to registration. * NOTE: QTc intervals will be corrected using Fridericia's formula. * REGISTRATION: Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only. * REGISTRATION: For persons of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for 6 months after the last dose of study treatment. * REGISTRATION: For persons able to father a child: agreement to remain abstinent (refrain from heterosexual intercourse with a person of childbearing potential) or use contraceptive measures, and agreement to refrain from donating sperm during the treatment period and for 6 months after the last dose of study treatment. * REGISTRATION: Provide written informed consent. * REGISTRATION: Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study). * REGISTRATION: Willing to provide tissue, blood, and stool samples for correlative research purposes. * REGISTRATION: Arm C Only: Negative serology for acute Epstein-Barr virus (EBV) infection (negative EBV viral capsid antigen \[VCA\] immunoglobulin M \[IgM\]). Exclusion Criteria: * PRE-REGISTRATION: Prior systemic anti-cancer therapy for melanoma (e.g., chemotherapy, hormonal therapy, targeted therapy, immunotherapy including anti-PD-1, anti-PDL1 agents, or other biologic therapies), with the following exceptions: adjuvant treatment with interferon, IL-2, granulocyte-macrophage colony-stimulating factor (GM-CSF) or vaccine therapies are allowed, if discontinued \>= 28 days prior to pre-registration. * PRE-REGISTRATION: Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm. * PRE-REGISTRATION: For patients with concurrent diagnosis of primary melanoma with nodal involvement, major surgical procedure other than lymph node biopsy or wide local excision of primary melanoma =\< 4 weeks prior to pre-registration, or anticipation of need for a major surgical procedure for reasons other than melanoma during the course of the study. * PRE-REGISTRATION: For patients with nodal recurrence, surgical procedure or anti-cancer therapy for this recurrence (other than lymph node biopsy) or anticipation of need for a major surgical procedure for reasons other than melanoma during the course of the study. * PRE-REGISTRATION: Prior radiotherapy for melanoma. * PRE-REGISTRATION: History of non-nodal melanoma metastasis or central nervous system (CNS) lesion(s) proven or clinically suspected to be metastasis. * PRE-REGISTRATION: Active malignancy (other than melanoma) or malignancy =\< 3 years prior to pre-registration. * NOTE: Exceptions: Asymptomatic papillary thyroid cancer (not requiring treatment), resected basal cell carcinoma (BCC), resected cutaneous squamous cell carcinoma (SCC), resected carcinoma in situ of the cervix, resected carcinoma in situ of the breast, in situ prostate cancer, non-muscle-invasive bladder cancer, Stage I uterine cancer, or other curatively treated malignancies from which the patient has been disease-free for at least 3 years prior to pre registration. * PRE-REGISTRATION: Prior allogeneic stem cell or solid organ transplantation. * PRE-REGISTRATION: History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest CT scan. * PRE-REGISTRATION: History of autoimmune disease requiring systemic immunosuppressive or immune-modulatory therapy =\< 5 years prior to pre-registration. * NOTE: Exceptions are allowed for hypothyroidism on thyroid replacement therapy; or Type 1 diabetes on insulin regimen. * PRE-REGISTRATION: Active psoriasis requiring therapy (systemic or topical). * PRE-REGISTRATION: Known clinically significant liver disease, including alcoholism, cirrhosis, fatty liver, and other inherited liver disease as well as active viral disease. * PRE-REGISTRATION: Arms A and B only: History of or evidence of retinal pathology on ophthalmologic examination including but not limited to: * Neurosensory retinal detachment * Central serous chorioretinopathy * Retinal vein occlusion (RVO) * Neovascular macular degeneration * PRE-REGISTRATION: Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy. * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial. * PRE-REGISTRATION: Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection (including but not limited to tuberculosis) * Clinically significant cardiac dysfunction including: * Symptomatic congestive heart failure defined as New York Heart Association class II or higher * Unstable angina pectoris or new-onset angina =\< 3 months prior to pre-registration * Unstable cardiac arrhythmia * Myocardial infarction =\< 3 months prior to pre-registration * Congenital long QT syndrome * Clinically significant stroke, reversible ischemic neurological defect, or transient ischemic attack =\< 6 months prior to pre-registration * Any grade 3 hemorrhage or bleeding event =\< 4 weeks prior to pre-registration * Uncontrolled diabetes or symptomatic hyperglycemia * Psychiatric illness/social situations that, in the judgement of the investigator, would: a) limit compliance with study requirements, or b) make the patient inappropriate for entry into this study, or c) interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. * PRE-REGISTRATION: Known hypersensitivity to biopharmaceutical agents produced in Chinese hamster ovary cells (example \[ex\]: recombinant follicle-stimulating hormone \[FSH\]). * PRE-REGISTRATION: Known hypersensitivity to any components of the atezolizumab (all arms), tiragolumab (Arm C only), cobimetinib (Arms A and B only), or vemurafenib (Arms A and B only) formulations. * PRE-REGISTRATION: History of severe allergic, anaphylactic or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins. * REGISTRATION: Received anticancer treatments or investigational agents during pre-registration period. * REGISTRATION: Clinically suspected non-nodal metastatic melanoma. * REGISTRATION: Arm A only: For BRAF-mutant patients only: anticipated use of any concomitant medication =\< 7 days prior to registration that is known to cause QT prolongation (which may lead to torsade de pointes). * REGISTRATION: Arms A and B only: History of malabsorption or other clinically significant metabolic dysfunction that may interfere with absorption of oral study treatment or inability or unwillingness to swallow oral medication. * REGISTRATION: Signs or symptoms of infection or has received antibiotics =\< 14 days prior to registration. * NOTE: Patients receiving prophylactic antibiotics (e.g., to prevent a urinary tract infection or chronic obstructive pulmonary disease exacerbation) are eligible for the study. * REGISTRATION: Any of the following because this study involves investigational agents whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ adequate contraception * REGISTRATION: Treatment with a live, attenuated vaccine =\< 4 weeks prior to registration, or anticipation of need for such a vaccine during the course of the study. * REGISTRATION: Treatment with systemic immunosuppressive medication (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor (TNF)-alpha agents) =\< 2 weeks prior to registration, or anticipation of need for systemic immunosuppressive medication during the course of the study. * NOTE: Patients who have received acute, low-dose systemic steroids (=\< 10 mg/day oral prednisone or equivalent) prior to registration or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) are eligible for the study. * NOTE: The use of inhaled corticosteroids for chronic obstructive pulmonary disease or asthma, mineralocorticoids (e.g., fludrocortisone), or low-dose corticosteroids for patients with orthostatic hypotension or adrenocortical insufficiency is allowed. * REGISTRATION: Requirement for concomitant therapy or food that is prohibited during the study. * REGISTRATION: Arms A and B only: Inability to abstain from alcohol during neoadjuvant phase. * REGISTRATION: Arm C only: Known Epstein-Barr virus (EBV) infection. * NOTE: Patients with symptoms such as splenomegaly, fever, sore throat, non-malignant cervical lymphadenopathy, and/or tonsillar exudate, should undergo an EBV polymerase chain reaction (PCR) test to screen for acute infection or suspected chronic active infection. Patients with a positive EBV PCR test are excluded.