SJDAWN: St. Jude Children's Research Hospital Phase 1 Study Evaluating Molecularly-Driven Doublet Therapies for Children and Young Adults With Recurrent Brain Tumors

Potential participants will first be screened using the screening inclusion/exclusion shown below. If they meet the requirements of the screening phase, they will then be evaluated for enrollment based on the overall study's inclusion criteria as well as the stratum-specific inclusion/exclusion criteria for the applicable stratum, all of which are shown below. SCREENING INCLUSION CRITERIA - ALL PARTICIPANTS: * Participants with recurrent, progressive, or refractory brain tumors. * Age ≥ 1 year and \< 25 years at the time of screening. Exception: Participants with recurrent, progressive, or refractory Medulloblastoma and are ≥ 1 and \< 40 years of age at the time of study screening are eligible for screening. * Participants and/or guardian have the ability to understand and the willingness to sign a written informed consent document according to institutional guidelines. SCREENING EXCLUSION CRITERIA - ALL PARTICIPANTS: * Participants with a diagnosis of recurrent, progressive, or refractory low grade glioma (LGG). * Previous exposure to a CDK4/6 inhibitor (palbociclib, abemaciclib, or ribociclib). * Participants with a history of clinically significant, uncontrolled heart disease and/or repolarization abnormalities. * Participants with any history of QTc prolongation (i.e. QTc interval of \> 450 msec). Participants who meet the requirements of the screening phase will then be evaluated for enrollment based on the overall study's inclusion criteria as well as the stratum-specific inclusion/exclusion criteria for the applicable stratum, all of which are shown below. INCLUSION CRITERIA - OVERALL STUDY - ALL PARTICIPANTS: * Evaluable disease, as defined as meeting any of the following: * Patients who have measurable disease * Patients with radiologically discernible but non-measurable lesions (i.e. leptomeningeal disease) * Patients with CSF positive disease * Participants must have received their last dose of anticancer therapy (including experimental) at least 4 weeks prior to study enrollment. * Note: Participants must have relapsed with recurrent, progressive or refractory disease on or after any prior anticancer therapy. * Participants must have had their last fraction of radiation at least 4 weeks prior to study enrollment. Participants who received radiation therapy for palliation must have had their last fraction of radiation at least 2 weeks prior to study enrollment. * Note: Participants must have relapsed with recurrent, progressive or refractory disease after any prior radiation therapy that is not considered palliative. Palliative radiation therapy is defined as local small port RT to alleviate and/or palliate symptoms. (CSI, whole brain RT, large field/port RT, or large field/port multilevel spinal RT will not be considered palliative at any dose.) * Participants who are receiving corticosteroids must be on a stable or decreasing dose for at least 1 week prior to study enrollment with no plans for escalation. * Participants who are receiving known strong inducers and/or strong inhibitors of CYP3A4/5, drugs that have a narrow therapeutic window and are predominantly metabolized through CYP3A4/5, and medications that carry a known risk for QT prolongation must discontinue these drugs at least 7 days prior to study enrollment. * Participants must discontinue herbal preparations, herbal medication, and dietary supplements, with the exception of multivitamins, at least 7 days prior to study enrollment. * Participants must be able to swallow medication. It is acceptable to administer medication via a g-tube if participant has a g-tube. It is not acceptable to place a g-tube for the purpose of delivering study medication. * Participants must have a Lansky (≤ 16 years) or Karnofsky (\> 16 years) score of at least 50 and, in the opinion of the investigator, a minimum life expectancy of at least 6 weeks at the time of study enrollment. * Note: 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. * Participant must have adequate bone marrow and organ function defined as: * ANC ≥ 1000/mm3 without growth factor support within 7 days of the test * Platelet count ≥ 50,000/mm\^3 without support of a platelet transfusion within 7 days of the test * Hemoglobin ≥ 8.0 g/dL without support of a blood transfusion within 7 days of the test * Creatinine clearance ≥ 70 mL/min/1.73 m\^2 or serum creatinine ≤ the maximum serum creatinine based on age/gender (threshold creatinine values derived from the Schwartz formula for estimating GFR utilizing child length and stature data published by the Centers for Disease Control and Prevention or creatinine clearance ≥70 mL/min/1.73 m\^2). * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x ULN. For the purposes of eligibility the ULN of ALT and AST is 45 U/L. * Total bilirubin ≤ ULN or if \> ULN then direct bilirubin ≤ 1.5xULN. * Participants and/or guardian have the ability to understand and the willingness to sign a written informed consent document according to institutional guidelines. EXCLUSION CRITERIA - OVERALL STUDY - ALL PARTICIPANTS: * Participants receiving any other investigational agents. * Participants with other clinically significant medical disorders (serious infections or significant cardiac, pulmonary, hepatic, psychiatric, GI disease, or other organ dysfunction) that in the investigator's judgment could compromise their ability to tolerate or absorb protocol therapy or would interfere with the study procedures or results. * Female participants who are breastfeeding a child. * Participants with QTc interval of \> 450 msec on screening ECG. * Participants with a pathogenic somatic or known germline retinoblastoma (RB1) gene mutation. (A) INCLUSION CRITERIA - STRATUM A PARTICIPANTS ONLY: * Participants with recurrent, progressive, or refractory Non-WNT Non-SHH (NWNS) Medulloblastoma or Ependymoma as confirmed through central pathology review. * Age ≥ 1 year and \< 25 years at the time of enrollment. * Female participants of childbearing potential must have a negative pregnancy test at the time of enrollment on this study and be willing to use a highly effective method of contraception throughout the study and for 16 weeks after discontinuation of the study drug. * Male participants of child fathering potential must be willing to use medically acceptable form of contraception during treatment and for 16 weeks after stopping treatment. (A) EXCLUSION CRITERIA - STRATUM A PARTICIPANTS ONLY: * Participants with subependymoma or myxopapillary ependymoma. (B) INCLUSION CRITERIA - STRATUM B PARTICIPANTS ONLY: * Participants with recurrent, progressive, or refractory CNS tumors as confirmed through central pathology review and whose diagnosis is being treated on this study. * Age ≥ 1 year and \< 25 years at the time of study enrollment. * Must meet the following weight and BSA restrictions: * For enrollment on dose levels 0A, must have a weight ≥16kg and \<32kg. * For enrollment on dose level 0B, must have a weight of ≥32kg and BSA ≥ 0.55m\^2. * For enrollment on dose level 1, must have a weight ≥16kg and BSA ≥0.55m\^2. * For enrollment on dose level 2, must have a weight ≥16kg and BSA≥ 0.63m\^2 * For enrollment on dose levels 3 or 4A, must have a weight ≥16kg * For enrollment on dose levels 4B or 5, must have a weight ≥20kg and ≤106kg * Participant must be able to swallow trametinib tablets. * Female participants of childbearing potential must have a negative pregnancy test at the time of enrollment on this study and be willing to use a highly effective method of contraception throughout the study and for 16 weeks after discontinuation of the study drug. * Male participants of child fathering potential must be willing to use medically acceptable form of contraception during treatment and for 16 weeks after stopping treatment. (B) EXCLUSION CRITERIA - STRATUM B PARTICIPANTS ONLY: Participants eligible for this study must NOT meet ANY of the following criteria. * Participants with Low Grade Glioma (LGG) or Diffuse Intrinsic Pontine Glioma (DIPG). * Previous exposure to a MEK inhibitor (i.e. trametinib, selumetinib). * Participants with abnormal LVEF on screening, defined as \> 10% below lower limit of normal on screening. * Participants with retinal vein occlusion (RVO). * Previous exposure to a MEK inhibitor (i.e., trametinib, selumetinib. (C) INCLUSION CRITERIA - STRATUM C PARTICIPANTS ONLY: * Participants with recurrent, progressive, or refractory SHH Medulloblastoma and presence of either a or b as confirmed by central pathology review of the tumor specimen: a) copy number loss of 9q b) PTCH1 mutation and whose diagnosis is being treated on this study. * Age ≥ 10 years and \<40 years at the time of study enrollment. * Participant must be skeletally mature as defined as females with a bone age ≥ 15 years (180 months) and males with a bone age ≥ 17 years (204 months). This includes participants that are within 2 standard deviations of this value (i.e. if SD = 11 months on bone age; then a male patient who has a bone age of 182 months would be eligible; or a female patient with a bone age of 158 months.) * Female participants of childbearing potential must have a negative pregnancy test at the time of enrollment on this study and be willing to use a highly effective method of contraception throughout the study and for 8 months after discontinuation of the study drug. * Male participants of child fathering potential must be willing to use medically acceptable form of contraception during treatment and for 8 months after stopping treatment. (C) EXCLUSION CRITERIA - STRATUM C: * Exposure to smoothened inhibitor (vismodegib, sonidegib) within the last 6 months.