Phase 2 Study of Alisertib Therapy for Rhabdoid Tumors

We propose a study with 3 primary treatment strata according to participant's previous treatment, age and presence of extra-CNS disease, with substrata for presence of focal or metastatic disease: \* STRATUM A - RECURRENT OR PROGRESSIVE DISEASE: Patients \< 22 years of age at diagnosis with recurrent or progressive MRT (either CNS and/or extra-CNS) and measurable disease as defined in the protocol. * Stratum A1: patients with AT/RT (CNS MRT). * Stratum A2: patients with extra-CNS MRT (patients with concurrent progression of AT/RT and MRT are eligible for therapy, but their data will be analyzed separately). * Stratum A3: patients with synchronous AT/RT and extra-CNS MRT Stratum A is Closed to Accrual \* STRATUM B - NEWLY DIAGNOSED DISEASE IN YOUNG CHILDREN \< 36 MONTHS: Patients \< 36 months of age at diagnosis of CNS-AT/RT, no prior therapy: * Stratum B1: Patients with no metastatic disease (M0). * Stratum B2: Patients with metastatic disease (M+) regardless of degree of resection. * Stratum B3: Patients for whom CSF by lumbar puncture was not obtained for clinical reasons and have no other evidence of metastatic disease (MX). Stratum B is Closed to Accrual \* STRATUM C - NEWLY DIAGNOSED DISEASE IN CHILDREN \> 3 YEARS: Patients \> 3 years (36 months) of age at diagnosis of AT/RT, no prior therapy: * Stratum C1: Patients with gross total (GTR) or near total resection (NTR) defined as \<1.5 cm2 of residual tumor, and no metastatic disease. * Stratum C2: Patients with metastatic disease (M+) and/or bulky residual tumor \>1.5 cm\^2. STRATUM D - SYNCHRONOUS EXTRANEURAL AT/RT and EXTRA-CNS MRT: Treatment will be based on the extent of both CNS and extra-CNS disease. CNS-directed therapy will be given according to Strata B1, B2, C1 or C2 according to age and metastatic status. In addition, patients may receive irradiation according to best clinical management for local control of extra-CNS disease. * Stratum D1: Patients \< 36 months at time of diagnosis with synchronous AT/RT and extra-CNS MRT and no metastatic CNS disease (M0). * Stratum D2: Patients \< 36 months at time of diagnosis with synchronous AT/RT and extra- CNS MRT and metastatic CNS disease (M+). * Stratum D3: Patients \< 36 months at time of diagnosis with synchronous AT/RT and extra-CNS MRT for whom CSF by lumbar puncture was not obtained for clinical reasons and without other evidence of metastatic disease (MX) * Stratum D4: Patients ≥ 36 months at time of diagnosis with synchronous extra-CNS MRT with or without metastatic CNS disease regardless of the degree of tumor resection. Stratums D1, D2 and D3 are Closed to Accrual Biological parents of participants with ATRT/MRT may consent to and provide a genomic blood specimen for DNA extraction and analysis. OVERVIEW OF TREATMENT PLAN: Patients with recurrent disease (Stratum A) will receive alisertib as a single agent days 1-7 out of 21 days. Newly diagnosed patients (Strata B, C and D) will receive alisertib in sequence with chemo and radiotherapy. Patients on sub-strata B1 and D1 will receive focal RT once they are \>12 months of age. Patients on sub-strata B2 and D2, with disseminated disease will not receive CNS radiation therapy (RT). Patients on sub-strata C1/C2/D4 will receive risk-stratified craniospinal irradiation (CSI) and boost to primary tumor site followed by adjuvant chemotherapy. Patients on sub-strata B3 and D3 will receive therapy similar to sub-strata B2 and D2 and will be considered for local radiotherapy depending on their age, response to therapy, and subsequent metastatic staging. Those patients with concurrent CNS and extra-CNS MRT may undergo irradiation of the extra-CNS MRT according to best clinical management in addition to CNS directed therapy. Alisertib will be administered only to eligible patients under the supervision of the investigator or identified sub-investigator(s).