Savolitinib in Treating Patients With Recurrent or Refractory Primary CNS Tumors

Inclusion Criteria: * Patients with a histologically confirmed diagnosis of a primary CNS tumor (medulloblastoma, high-grade glioma, or diffuse intrinsic pontine glioma \[DIPG\]) that is recurrent, refractory, or progressive. All tumors must have histologic verification at either the time of diagnosis or recurrence except patients with diffuse intrinsic brain stem tumors. These patients must have radiographic or clinical evidence of progression. Patients with a recurrent, progressive, or refractory primary CNS tumor with evidence of genetic activation of the MET pathway, regardless of histology, are also eligible to the Phase I component of this study * Note: Refractory disease is defined as the presence of persistent abnormality on conventional MRI imaging that is further distinguished by histology (biopsy or sample of lesion) or advanced imaging, OR as determined by the treating physician and discussed with the primary investigator prior to enrollment * Efficacy Expansion Cohort: Patients must have a recurrent, progressive, or refractory primary CNS tumor with evidence of genetic activation of the MET pathway, regardless of histology. Specimens can be from diagnosis or recurrence and there is no time limit from when the specimen was obtained prior to enrollment onto the efficacy expansion cohort. Results from a Clinical Laboratory Improvement Act (CLIA)-certified laboratory will be accepted for this eligibility criterion. Sites must provide a redacted copy of the local CLIA-certified sequencing laboratory report to the study chair via email prior to enrollment. MET pathway activation is defined as: * MET mutations, OR * MET or HGF amplification, OR * MET fusion * Recurrent or refractory primary malignant CNS tumor patients must have adequate pre-trial frozen or formalin-fixed paraffin-embedded (FFPE) tumor material available for the required correlative studies. If target amounts of tissue or number of slides are not available, the site must obtain study chair/co-chair approval for adequacy of submitted tumor samples and prioritization of studies to be performed, prior to patient enrollment * Patients with DIPG who have pre-trial tumor tissue available are requested to submit tissue; however, this is not required for eligibility * Patients must have evaluable disease to be eligible. Evaluable disease is defined as the presence of at least one lesion that can be measured accurately in at least 2 (two) dimensions * Patients must be \> 5 years and =\< 21 years of age at the time of study enrollment * Body surface area (BSA) * Patients enrolled on 75 mg/m\^2/day (dose level 0) must have a BSA \>= 1.00 m\^2 * Patients enrolled on 150 mg/m\^2/day (dose level 1) must have a BSA \>= 0.55 m\^2 * Patients enrolled on 240 mg/m\^2/day (dose level 2) must have a BSA \>= 0.67 m\^2 * Patients enrolled on 350 mg/m\^2/day (dose level 3) must have a BSA \>= 0.73 m\^2 * Patients must have failed prior standard therapy for their tumor. Patients with medulloblastoma must have received radiation therapy in addition to platinum and alkylator-based chemotherapy. Patients with high-grade glioma (HGG) and DIPG must have at least received radiation therapy. Patients must have recovered from the acute treatment related toxicities (defined as =\< grade 1 if not defined in eligibility criteria) of all prior chemotherapy, immunotherapy, radiotherapy, or any other treatment modality prior to entering this study * Patients must have received their last dose of known myelosuppressive anticancer therapy at least 21 days prior to enrollment or at least 42 days if it included nitrosourea * Biologic or investigational agent (anti-neoplastic): * Patients must have recovered from any acute toxicity potentially related to the agent and received their last dose of the investigational or biologic agent \>= 7 days prior to study enrollment * For agents 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 Monoclonal antibody treatment and agents with known prolonged half-lives: * Patients must have recovered from any acute toxicity potentially related to the agent and received their last dose of the agent \>= 28 days prior to study enrollment * Patients must have had their last fraction of: * Craniospinal irradiation or total body irradiation or radiation to \>= 50% of pelvis \> 12 weeks prior to enrollment * Focal irradiation \> 4 weeks prior to enrollment * Patients must be: * \>= 24 weeks since allogeneic stem cell transplant prior to enrollment with no evidence of active graft versus (vs.) host disease * \>= 12 weeks since autologous stem cell transplant prior to enrollment * Neurologic Status * Patients with neurological deficits should have deficits that are stable for a minimum of 1 week prior to enrollment. A baseline detailed neurological exam should clearly document the neurological status of the patient at the time of enrollment on the study * Patients with seizure disorders may be enrolled if seizures are well controlled * Patients must be able to swallow whole tablets to be eligible for study enrollment * Karnofsky performance scale (KPS for \> 16 years of age) or Lansky performance score (LPS for =\< 16 years of age) assessed within two weeks of enrollment must be \>= 50 * Patients who are unable to walk because of neurologic deficits, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Absolute neutrophil count \>= 1.0 x 10\^9 cells/ L * Platelets \>= 100 x 10\^9 cells/ L (unsupported, defined as no platelet transfusion within 7 days prior to enrollment) * Hemoglobin \>= 8 g/dL (hemoglobin should be unsupported, i.e., red blood cell transfusions are not allowed within 14 days prior to enrollment) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x the upper limit of normal (ULN) with total bilirubin =\< 1x ULN OR total bilirubin \> ULN - =\< 1.5 x ULN with ALT and AST =\< 1 x ULN * Albumin \>= 2 g/dL * Serum creatinine based on age/sex. Patients that do not meet the criteria below but have a 24 hour creatinine clearance or glomerular filtration rate (GFR) (radioisotope or iothalamate) \>= 70 mL/min/1.73 m\^2 are eligible * Age: Maximum serum creatinine (mg/dL) * 2 to \< 6 years: 0.8 (male and female) * 6 to \< 10 years: 1 (male and female) * 10 to \< 13 years: 1.2 (male and female) * 13 to \< 16 years: 1.5 (male), 1.4 (female) * \>= 16 years: 1.7 (male), 1.4 (female) * International normalized ratio (INR) \< 1.5 x ULN and activated partial thromboplastin time (aPTT) \< 1.5 x ULN unless patients are receiving therapeutic anti-coagulation which affects these parameters * Patients with known tumor thrombus or deep vein thrombosis are eligible if clinically stable on low molecular weight heparin for \>= 2 weeks * Cardiac function: * Mean resting corrected QT interval (QTc Bazett) =\< 450 msec on screening obtained from 3 electrocardiograms (EKGs) * Oxygen saturation as measured by pulse oximetry is \> 93% on room air * Patients who are receiving corticosteroids must be on a stable or decreasing dose for at least 1 week prior to enrollment * Patients must be off all colony-stimulating factor(s) (e.g., filgrastim, sargramostim or erythropoietin) for at least 1 week prior to enrollment. Two (2) weeks must have elapsed if patients received polyethylene glycol (PEG) formulations * Pregnancy Prevention * Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study * Women of child-bearing potential should use effective contraception from the time of enrollment until 4 weeks after discontinuing study treatment * Male study participants should use a condom with female partners of child-bearing potential during the study and for 24 weeks after discontinuing study treatment * If the female partner of a male study participant is not using effective contraception, men must use a condom during the study and for 24 weeks after discontinuing study treatment * Male study participants should avoid fathering a child and refrain from sperm donation from study start to 24 weeks after discontinuing study treatment * Ability to understand and willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants Exclusion Criteria: * Pregnant women or nursing mothers are excluded from this study. Female patients of childbearing potential must have a negative serum or urine pregnancy test within 7 days prior to enrollment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. Pregnant women are excluded from this study because there are unknown but potential risks to an unborn baby from savolitinib. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with savolitinib, breastfeeding should be discontinued if the mother is treated with savolitinib * Patients with a known serious active infection including, but not limited to human immunodeficiency virus, and tuberculosis * Patients with a known active or resolved viral hepatitis infection * Patients with any clinically significant unrelated systemic illness or significant cardiac, pulmonary, hepatic, or other organ dysfunction), that in the opinion of the investigator would compromise the patient's ability to tolerate protocol therapy, put them at additional risk for toxicity or would interfere with the study procedures or results * Patients with uncontrolled hypertension (i.e., a blood pressure \[BP\] \> 95th percentile for age, height, and sex, patients with values above these levels must have their blood pressure controlled with medication prior to starting study drug) * The normal blood pressure by height, age, and sex can be assessed by using the NIH Guidelines on the PBTC Member's website (Protocols- Generic Forms and Templates- Normal Blood Pressure by Height and Age) * Patients with any of the following cardiac diseases * Congestive heart failure (New York Heart Association \>= grade 2) * Clinically significant cardiac arrhythmia * Mean resting corrected QT interval (QTc Bazett) \> 450 msec on screening obtained from 3 electrocardiograms (EKGs) or * Factors that may increase the risk of QTc prolongation such as chronic hypokalemia not correctable with supplements, congenital or familial long QT syndrome, or * Family history of unexplained sudden death under 40 years of age in first-degree relatives or * Any concomitant medication known to prolong the QT interval and cause Torsade de Pointes. These drugs must have been discontinued prior to the start of administration of study treatment in accordance with guidance * Any clinically important abnormalities in rhythm, conduction, or morphology of resting EKG, e.g., complete left bundle branch block, third degree heart block, second degree heart block, PR interval \> 250 msec * Patients with history of liver cirrhosis of any origin and clinical stage; or history of other serious liver disease or chronic disease with relevant liver involvement, with or without normal liver function tests (LFTs), including but not limited to: * Hemochromatosis * Alpha -1 antitrypsin deficiency * Autoimmune hepatitis (AIH) * Primary sclerosing cholangitis (PSC) * Primary biliary cirrhosis (PBC) * Biopsy-confirmed non-alcoholic steatohepatitis (NASH) with advanced fibrosis * Biopsy-confirmed alcoholic steatohepatitis with advanced fibrosis * Wilson's disease * Hepatocellular carcinoma * Patients with liver metastases are eligible, provided they meet other eligibility criteria, including liver biochemistry criteria * Patients with a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen for this trial * Concurrent Therapy * Patients who are receiving any other anticancer or investigational drug therapy * Patients receiving strong inducers of CYP3A4, strong inhibitors of CYP3A4 or CYP1A2 or CYP3A4 substrates with a narrow therapeutic index within 2 weeks of the first dose of savolitinib (3 weeks for St John's Wort). Strong inducers of CYP3A4 and CYP3A4 substrates which have a narrow therapeutic range or CYP3A4 sensitive substrates should not be used during the trial or used with caution. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. Patient drug information handout and wallet card should be provided to patients * Prior or current treatment with a MET inhibitor (e.g., foretinib, crizotinib, cabozantinib, or onartuzumab) * Patient is currently receiving any of the following herbal preparations or medications and cannot be discontinued 1 week (7 days) prior to enrollment (3 weeks for St. John's wort). These herbal medications include, but are not limited to: cannabis products, St. John's wort, kava, ephedra (ma huang), gingko biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto, and ginseng * Patient has undergone major surgical procedure =\< 28 days prior to beginning study drug or a minor surgical procedure =\< 7 days prior to beginning study drug. No waiting is required following port-a-cath placement * Patients who in the opinion of the investigator are unwilling or unable to return for required follow-up visits or obtain follow-up studies required to assess toxicity to therapy or to adhere to drug administration plan, other study procedures, and study restrictions * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition * Prisoners will be excluded from this study