This phase II trial studies how well vemurafenib and cobimetinib work in treating patients with BRAF V600E mutation positive craniopharyngioma. Vemurafenib and cobimetinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

PRIMARY OBJECTIVES:

I. To determine the activity of BRAF and MEK inhibitor combination in untreated papillary craniopharyngiomas as measured by best response at any time during the first four cycles of BRAF and MEK inhibitor treatment.

II. To determine the activity of BRAF and MEK inhibitor combination in papillary craniopharyngiomas that have progressed after prior radiation treatment with or without surgical resection as measured by best response at any time during the first four cycles of BRAF and MEK inhibitor treatment.

SECONDARY OBJECTIVES:

I. To determine the progression-free survival of patients with papillary craniopharyngiomas receiving BRAF and MEK inhibitors.

II. To determine the toxicity of BRAF/MEK inhibitors in patients with papillary craniopharyngiomas.

III. To determine the activity of BRAF and MEK inhibitor combination in papillary craniopharyngiomas as measured by response of enhancing volume of craniopharyngioma.

IV. To determine the activity of BRAF and MEK inhibitor combination in papillary craniopharyngiomas as measured by response of nonenhancing volume of craniopharyngioma.

V. To determine the overall survival of patients with papillary craniopharyngiomas receiving BRAF and MEK inhibitors.

VI. To determine the duration of response in patients with papillary craniopharyngiomas receiving BRAF and MEK inhibitors.

TERTIARY OBJECTIVES:

I. To evaluate visual fields in patients with papillary craniopharyngiomas who have received BRAF/MEK inhibitors.

II. To evaluate pituitary hormone replacement over time in patients with papillary craniopharyngiomas who have received BRAF/MEK inhibitors.

III. To evaluate the time to response in patients with papillary craniopharyngiomas receiving BRAF and MEK inhibitors.

IV. To assess toxicity that may be associated with radiotherapy in patients with papillary craniopharyngiomas who have received BRAF/MEK inhibitors.

V. To evaluate molecular biomarkers of response in papillary craniopharyngiomas.

VI. To evaluate circulating tumor cells and cell-free circulating deoxyribonucleic acid (DNA) in patients with papillary craniopharyngiomas.

OUTLINE:

Patients receive vemurafenib orally (PO) twice daily (BID) on day 1-28 and cobimetinib PO once daily (QD) on days 1-21. Treatment repeats every 28 days for up to 5 courses in the absence of disease progression or unacceptable toxicity. Patients may then receive radiation therapy, surgery, or continued treatment with vemurafenib and cobimetinib at the discretion of the treating physician.

After completion of study treatment, patients with disease progression are followed up every 16 weeks for 2 years and all other patients are followed up every 6 months for 5 years.

• Pre-registration: Patients must have local diagnosis of papillary craniopharyngioma and have tissue slides available for submission to central pathology review; central pathology review will include immunohistochemistry (IHC) testing for BRAF V600E mutation (VE1 clone) and beta-catenin IHC (membranous, non-nuclear pattern) if needed to confirm diagnosis of papillary craniopharyngioma

• Histologically proven papillary craniopharyngioma as documented by central pathology review with positive BRAF V600E mutation by IHC

• Measurable disease and/or non-measurable disease

  • Measurable disease, defined as bidimensionally measurable lesions with clearly defined margins by magnetic resonance imaging (MRI) scans, with a minimum diameter of 10 mm in both dimensions
  • Progressive disease required in cohort B, defined as an increase in the bidirectional area by 25% within the past 13 months after surgery or radiation; progressive or recurrent disease is not required in cohort A, but is allowed provided it is a new diagnosis and patient has not received prior treatment.

• Prior treatment

  • Cohort A: No prior therapy received other than surgery

  • Cohort B: Prior radiation therapy required (any type of prior radiation is allowed)

    • For patients treated with external beam radiation therapy, interstitial brachytherapy or radiosurgery, an interval of >= 3 months must have elapsed from completion of radiation therapy to registration
    • Recovered to Common Terminology Criteria for Adverse Events (CTCAE) grade 1 or less toxicity attributed to radiation with exception of alopecia, fatigue

  • For patients enrolling on Cohort A or Cohort B:

    • For patients treated with surgery, an interval of >= 21 days must have elapsed prior to registration
    • No prior treatment with BRAF or MEK inhibitors
    • Steroid dosing stable for at least 4 days prior to registration

• Not pregnant and not nursing; for women of childbearing potential only, a negative pregnancy test done =< 7 days prior to registration is required

• ECOG performance status =< 2

• Comorbid conditions

  • No evidence of active bleeding, bleeding diathesis, or hemoptysis (>= 1/2 teaspoon of red blood) =< 8 weeks prior to registration
  • No evidence of intracranial hemorrhage =< 4 weeks prior to registration
  • Patients who have experienced thromboembolic event within 6 months prior to registration must be on stable therapeutic anticoagulation for at least 4 weeks prior to registration
  • No symptomatic congestive heart failure (New York Heart Association class II, III, or IV) within 6 months prior to registration
  • No current unstable angina or uncontrolled arrhythmia
  • No uncontrolled hypertension at time of registration (blood pressure [BP] > 150/95 despite antihypertensive therapy)
  • No known history of prolonged QT syndrome
  • No known history of ventricular arrhythmia within 6 months of registration
  • No known history of uveitis or iritis =< 4 weeks prior to registration
  • No known history of or evidence of retinal pathology that is considered a risk factor for neurosensory retinal detachment, retinal vein occlusion (RVO), or neovascular macular degeneration within 12 months of registration
  • No known history of chronic lung disease

• Concomitant medications

  • Chronic concomitant treatment with strong CYP3A4 inducers or CYP3A4 inhibitors is not allowed; patients must discontinue the drug at least 14 days prior to study registration
  • Chronic concomitant treatment with CYP1A2 substrate is not allowed; patients must discontinue the drug at least 14 days prior to study registration

• Absolute neutrophil count >= 1500/mm^3

• Platelets >= 100,000/mm^3

• Creatinine =< 1.5 mg/dL OR creatinine clearance >= 45mL/min

• Bilirubin =< 1.5 upper limit of normal (ULN)

• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 2.5 ULN