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

Patients will be stratified by the molecular and histologic characteristics of their tumor to one of three treatment strata. STRATUM A: * Combination Treatment: ribociclib and gemcitabine. * Patient Population: Participants with a diagnosis of refractory or recurrent medulloblastoma (Group 3/4) or refractory or recurrent ependymoma (including: ependymoma, not otherwise specified (NOS), WHO Grade III; ependymoma, RELA fusion positive; anaplastic ependymoma; ependymoma, NOS, WHO grade II). STRATUM B: * Combination Treatment: ribociclib and trametinib. * Patient Population: Participants with a diagnosis of one of the following refractory or recurrent CNS diseases: medulloblastoma \[sonic hedgehog (SHH)\], medulloblastoma (WNT), high grade glioma (including: high grade glioma, (NOS), WHO Grade III or IV; anaplastic astrocytoma, IDH mutant; glioblastoma, IDH-wildtype; glioblastoma, IDH-mutant; diffuse midline glioma, H3K27-mutant; anaplastic oligodendroglioma, IDH mutant and 1p/19q-codeleted; anaplastic pleomorphic xanthoastrocytoma) or select central nervous system (CNS) embryonal tumors (including: embryonal tumors with multilayered rosettes, C19MC-altered; embryonal tumors with multilayered rosettes, not otherwise specified (NOS); medulloepithelioma; CNS neuroblastoma; CNS ganglioneuroblastoma; CNS embryonal tumor, NOS; atypical teratoid/rhabdoid tumor; CNS embryonal tumor with rhabdoid features). STRATUM C: * Combination Treatment: ribociclib and sonidegib. * Patient Populations: Participants with refractory or recurrent medulloblastoma (SHH) \>6 months off smoothened inhibitor, presence of 9q loss or PTCH1 mutant, skeletally mature. The rolling 6 design will be used separately in each stratum to estimate the MTD or RP2D and determine the dose-limiting toxicity (DLT) of the combination of escalating doses. Therapy will be administered in cycles of 28 days and may be continued for up to 24 months (26 cycles) in the absence of disease progression or unacceptable toxicity. Stratum A participants may continue therapy past 24 months in absence of disease progression or unacceptable toxicity. Patients will receive doublet therapy in cycles of 28 days. The dose-limiting toxicity (DLT)-evaluation period will consist of the first cycle (i.e. first 4 weeks of therapy). Research participants will be evaluated at least once a week during the DLT-evaluation period and at regular intervals thereafter. Standard (e.g., physical exam, blood tests, and disease evaluations) tests will be obtained at regular intervals. Research-associated evaluations (e.g., pharmacokinetic studies, etc.) will also be obtained during therapy. Treatment may be continued for up to 2 years in the absence of disease progression or unacceptable toxicity. Stratum A participants may continue past 2 years in the absence of disease progression or unacceptable toxicity.