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 …