Inclusion Criteria:

          -  Patient must have enrolled onto APEC1621SC and must have been given a treatment
             assignment to Molecular Analysis for Therapy Choice (MATCH) to APEC1621G based on the
             presence of a BRAF V600 mutation

          -  Patients must have a body surface area >= 0.55 m^2 at enrollment; patients < 0.73 m^2
             must follow the dosing nomogram; patients >= 0.73 m^2 at enrollment must follow the
             dosing nomogram

          -  Patients must have radiographically measurable disease at the time of study
             enrollment; patients with neuroblastoma who do not have measurable disease but have
             metaiodobenzylguanidine (MIBG) positive (+) evaluable disease are eligible; measurable
             disease in patients with CNS involvement is defined as tumor that is measurable in two
             perpendicular diameters on magnetic resonance imaging (MRI) and visible on more than
             one slice; Note: The following do not qualify as measurable disease:

               -  Malignant fluid collections (e.g., ascites, pleural effusions)

               -  Bone marrow infiltration except that detected by MIBG scan for neuroblastoma

               -  Lesions only detected by nuclear medicine studies (e.g., bone, gallium or
                  positron emission tomography [PET] scans) except as noted for neuroblastoma

               -  Elevated tumor markers in plasma or cerebrospinal fluid (CSF)

               -  Previously radiated lesions that have not demonstrated clear progression post
                  radiation

               -  Leptomeningeal lesions that do not meet the measurement requirements for Response
                  Evaluation Criteria in Solid Tumors (RECIST) 1.1

          -  Karnofsky >= 50% for patients > 16 years of age and Lansky >= 50 for patients =< 16
             years of age; Note: Neurologic deficits in patients with CNS tumors must have been
             stable for at least 7 days prior to study enrollment; patients who are unable to walk
             because of paralysis, but who are up in a wheelchair, will be considered ambulatory
             for the purpose of assessing the performance score

          -  Patients must have fully recovered from the acute toxic effects of all prior
             anti-cancer therapy and must meet the following minimum duration from prior
             anti-cancer directed therapy prior to enrollment; if after the required timeframe, the
             numerical eligibility criteria are met, e.g. blood count criteria, the patient is
             considered to have recovered adequately

               -  Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive

                    -  >= 21 days after the last dose of cytotoxic or myelosuppressive chemotherapy
                       (42 days if prior nitrosourea)

               -  Anti-cancer agents not known to be myelosuppressive (e.g. not associated with
                  reduced platelet or absolute neutrophil count [ANC] counts): >= 7 days after the
                  last dose of agent

               -  Antibodies: >= 21 days must have elapsed from infusion of last dose of antibody,
                  and toxicity related to prior antibody therapy must be recovered to grade =< 1

               -  Corticosteroids: If used to modify immune adverse events related to prior
                  therapy, >= 14 days must have elapsed since last dose of corticosteroid

               -  Hematopoietic growth factors: >= 14 days after the last dose of a long-acting
                  growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor; for
                  growth factors that have known adverse events occurring beyond 7 days after
                  administration, this period must be extended beyond the time during which adverse
                  events are known to occur; the duration of this interval must be discussed with
                  the study chair and the study-assigned research coordinator

               -  Interleukins, interferons and cytokines (other than hematopoietic growth
                  factors): >= 21 days after the completion of interleukins, interferon or
                  cytokines (other than hematopoietic growth factors)

               -  Stem cell Infusions (with or without total-body irradiation [TBI]):

                    -  Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem
                       cell infusion including donor lymphocyte infusion (DLI) or boost infusion:
                       >= 84 days after infusion and no evidence of graft versus host disease
                       (GVHD)

                    -  Autologous stem cell infusion including boost infusion: >= 42 days

               -  Cellular therapy: >= 42 days after the completion of any type of cellular therapy
                  (e.g. modified T cells, natural killer [NK] cells, dendritic cells, etc.)

               -  Radiation therapy (XRT)/external beam irradiation including protons: >= 14 days
                  after local XRT; >= 150 days after TBI, craniospinal XRT or if radiation to >=
                  50% of the pelvis; >= 42 days if other substantial bone marrow (BM) radiation;
                  Note: Radiation may not be delivered to "measurable disease" tumor site(s) being
                  used to follow response to subprotocol treatment

               -  Radiopharmaceutical therapy (e.g., radiolabeled antibody, iobenguane I-131
                  [131I-MIBG]): >= 42 days after systemically administered radiopharmaceutical
                  therapy

               -  Patients must not have received prior exposure to a BRAF inhibitor (e.g.
                  vemurafenib, dabrafenib or encorafenib)

          -  For patients with solid tumors without known bone marrow involvement:

               -  Peripheral absolute neutrophil count (ANC) >= 1000/mm^3

               -  Platelet count >= 100,000/mm^3 (transfusion independent, defined as not receiving
                  platelet transfusions for at least 7 days prior to enrollment)

          -  Patients with known bone marrow metastatic disease will be eligible for study provided
             they meet the blood counts in above criteria (may receive transfusions provided they
             are not known to be refractory to red cell or platelet transfusions); these patients
             will not be evaluable for hematologic toxicity

          -  Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70
             ml/min/1.73 m^2 or a serum creatinine based on age/gender as follows:

               -  Age: 1 to < 2 years; maximum serum creatinine (mg/dL): male 0.6; female 0.6

               -  Age: 2 to < 6 years; maximum serum creatinine (mg/dL): male 0.8; female 0.8

               -  Age: 6 to < 10 years; maximum serum creatinine (mg/dL): male 1; female 1

               -  Age: 10 to < 13 years; maximum serum creatinine (mg/dL): male 1.2; female 1.2

               -  Age: 13 to < 16 years; maximum serum creatinine (mg/dL): male 1.5; female 1.4

               -  Age: >= 16 years; maximum serum creatinine (mg/dL): male 1.7; female 1.4

          -  Bilirubin (sum of conjugated + unconjugated) =< 1.5 x upper limit of normal (ULN) for
             age

          -  Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) =< 135
             U/L; (for the purpose of this study, the ULN for SGPT is 45 U/L)

          -  Serum albumin >= 2 g/dL

          -  Corrected QT (QTc) interval =< 480 milliseconds; Note: Patients should avoid
             concomitant medication known or suspected to prolong QTc interval or cause Torsades De
             Pointes; if possible, alternative agents should be considered; patients who are
             receiving drugs that prolong the QTc are eligible if the drug is necessary and no
             alternatives are available

          -  Patients must be able to swallow intact tablets

          -  All patients and/or their parents or legally authorized representatives must sign a
             written informed consent; assent, when appropriate, will be obtained according to
             institutional guidelines

        Exclusion Criteria:

          -  Pregnant or breast-feeding women will not be entered on this study due to risks of
             fetal and teratogenic adverse events as seen in animal/human studies; pregnancy tests
             must be obtained in girls who are post-menarchal; males or females of reproductive
             potential may not participate unless they have agreed to use an effective
             contraceptive method, for the duration of study treatment and for 6 months after the
             last dose of vemurafenib

          -  Patients receiving corticosteroids who have not been on a stable or decreasing dose of
             corticosteroid for at least 7 days prior to enrollment are not eligible; if used to
             modify immune adverse events related to prior therapy, >= 14 days must have elapsed
             since last dose of corticosteroid

          -  Patients who are currently receiving another investigational drug are not eligible

          -  Patients who are currently receiving other anti-cancer agents are not eligible

          -  Patients who are receiving cyclosporine, tacrolimus or other agents to prevent
             graft-versus-host disease post bone marrow transplant are not eligible for this trial

          -  Patients who are currently receiving drugs that are moderate to strong inducers or
             inhibitors of CYP3A4 are not eligible; moderate to strong inducers or inhibitors of
             CYP3A4 should be avoided from 14 days prior to enrollment to the end of the study;
             Note: CYP3A4 inducing anti-epileptic drugs and dexamethasone for CNS tumors or
             metastases, on a stable dose, are allowed

          -  Patients who are currently receiving drugs that are inhibitors or inducers of
             p-glycoprotein (P-gp) or adenosine triphosphate (ATP)-binding cassette, subfamily G,
             member 2 (ABCG2 [BCRP]) are not eligible

          -  Patients with known active cutaneous squamous cell carcinoma (includes keratoacanthoma
             or mixed keratoacanthoma subtype) are not eligible; patients who have fully excised
             lesions with dermatologic confirmation of absence of disease are eligible

          -  Patients with low grade glioma patients (World Health Organization [WHO] grades I and
             II) are not eligible

          -  Patients who have an uncontrolled infection are not eligible

          -  Patients who have received a prior solid organ transplantation are not eligible

          -  Patients who in the opinion of the investigator may not be able to comply with the
             safety monitoring requirements of the study are not eligible