Palbociclib Isethionate in Treating Younger Patients With Recurrent, Progressive, or Refractory Central Nervous System Tumors

Inclusion Criteria: * Patients with retinoblastoma protein (Rb1) positive recurrent, progressive or refractory central nervous system (CNS) tumors * Histologically confirmed Rb1 positive primary recurrent, progressive, or refractory central nervous system tumors; patients with low grade gliomas are excluded * Formalin fixed paraffin embedded tumor tissue (preferably from current recurrence) must be available to assess Rb1 protein status prior to enrollment; only patients with recurrent diffuse intrinsic brain stem glioma (DIPG) can be enrolled without the need for available tumor tissue for Rb1 protein status confirmation * Patients must have measurable disease (in 2-dimensions) on magnetic resonance imaging (MRI) scan of brain and/or spine to assess preliminary evidence of response * Body surface area (BSA): * Patients enrolled on dose level 1 (50 mg/m\^2) must have BSA \>= 1.20 m\^2 * Patients enrolled on dose level 2 (75 mg/m\^2) must have BSA \>= 0.93 m\^2 * Patients enrolled on dose level 3 (95 mg/m\^2) must have BSA \>= 0.70 m\^2 * Patients must have received no more than 2 prior chemotherapy regimens and/or focal radiotherapy for their brain tumor and fully recovered from the acute treatment related toxicities of all prior therapies prior to entering this study; for those acute baseline adverse events attributable to prior therapy, patients must meet organ function criteria * Chemotherapy: patients must have received their last dose of known myelosuppressive an…