A Study of Repotrectinib in Combination With Chemotherapy in Children and Young Adults With Solid Tumor Cancer

Inclusion Criteria (ALL Patients) : * Prior Therapy: Patients must have fully recovered from the acute toxic effects of all previous chemotherapy, immunotherapy, or radiotherapy prior to study enrollment. Patients must not have received the therapies indicated below for the specified time period prior to the first day of administration of protocol therapy on this study: * Myelosuppressive chemotherapy: Last dose was given at least 21 days before the start date for protocol therapy. * Biologic (anti-neoplastic agent including retinoids): Last dose given at least 7 days prior to the start date for protocol therapy. * Monoclonal antibodies: Last dose of any monoclonal antibodies must have received at least 7 days or 3 half-lives, whichever is longer, prior to the start date for protocol therapy. * Other immunotherapy (ex: tumor vaccine): Patient is eligible after 42 days of completion. Steroids are excluded from inclusion in immunotherapy. * Radiation Therapy: Patients must not have received radiation for a minimum of two weeks prior to first dose of the drug for small port. If extensive bone marrow radiation, at least 42 days must have elapsed. * Palliative radiotherapy on study is permitted for the treatment of painful bony lesions providing the lesions were known at the time of study entry and the Investigator clearly indicates that the need for palliative radiotherapy is not indicative of disease progression. In view of the current lack of data about the interaction of repotrectinib with radiotherapy, repotrectinib treatment should be interrupted during palliative radiotherapy, stopping 1 day before palliative radiotherapy and resuming treatment 1 day after completion of palliative radiotherapy and recovery from any acute radiation toxicities to baseline. * Hematopoietic Stem Cell Transplant (HSCT): Patients are eligible 12 weeks after date of autologous hematopoietic stem cell infusion following myeloablative therapy (timed from first day of this protocol therapy). Patients who have received an autologous hematopoietic stem cell infusion to support non- myeloablative therapy (such as \^131 I-MIBG) are eligible at any time as long as they meet the other criteria for eligibility. * \^131 I-MIBG therapy: A minimum of 6 weeks must have elapsed after \^131 I-MIBG therapy prior to start of protocol therapy. * Growth factors: Patients are eligible 14 days after last dose of long-acting growth factor (ex: peg-GCSF) or 7 days after short acting growth factor. * Any investigational agent or anticancer therapy other than chemotherapy and not otherwise noted: Not within 2 weeks prior to planned start of TPX-0005 (Repotrectinib) or 5 half-lives, whichever is shorter. Full recovery of clinically significant toxicities from that therapy must be evident. * Any prior treatment with a tyrosine kinase inhibitor (TKI) of ALK/ROS/NTRK does NOT exclude patient from study (Patients are eligible for study at least 7 days or 5 half-lives, whichever is shorter, after last dose) * Disease Status * Patients must have relapsed or refractory disease despite standard therapy. * Phase 1: Patients must have evaluable or measurable disease * Phase 2: All patients must have measurable disease (per Appendices 1-3) at time of enrollment * Exception: Patients with DIPG must have recurrent and/or progressive disease after upfront radiation therapy. Any number of prior recurrences is permitted. * Biopsy Requirement °Archived tissue must be available for analysis, but no fresh biopsy is required (exception: patients with DIPG do not require archived tissue). If no archival tissue is available, waiver may be permitted by study PI (phase 1 only). * Patients with Primary CNS Tumors: * Patients with primary CNS tumor or CNS metastases must be neurologically stable on a stable or decreasing dose of steroids for at least 14 days prior to enrollment * Archived tissue and histologic verification requirement are waived for patients with diffuse intrinsic pontine glioma (DIPG) * Performance Score: Patients must have a Lansky (\< 16 years age) or Karnofsky (≥ 16 years age) score of at least 50. Patients who are unable to walk because of paralysis or tumor pain, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. * No bone marrow involvement * Absolute Neutrophil Count ≥1000/mm\^3 (1 x 10\^9/L) * Platelet Count ≥100,000/mm \^3 (100 x 10\^9/L); transfusions allowed * Hemoglobin ≥ 8.0 g/dL, transfusions are allowed * Known bone marrow involvement (applicable for phase 2 only) * Absolute Neutrophil Count ≥750/mm 3 (0.75 x 10\^9/L) * Platelet Count ≥50,000/mm\^3 (100 x 10\^9/L), transfusions allowed * Hemoglobin ≥ 8.0 g/dL, transfusions are allowed * Serum Creatinine or Creatinine Clearance\*Creatinine within normal limits for age/gender (see table below) or creatinine clearance or nuclear GFR ≥ 60 mL/min/1.73m\^2 * Total Serum Bilirubin \<2.5 x ULN for age/gender * Liver Transaminases (AST/ALT) \<2.5 x ULN for age/gender; \< 5 x ULN for age/gender if liver metastasis is present * Serum calcium, magnesium and potassium Normal for age/gender or ≤ CTCAE Grade 1 with or without supplementation. * Cardiac Function Echocardiogram with left ventricular shortening fraction \>25% and QTc Friderica (QTcF) \</= 470ms on screening electrocardiogram * AST/ALT = aspartate aminotransferase/alanine aminotransferase, ULN = upper limit of normal * Adequate Renal Function using the Schwartz formula for estimating GFR Schwartz et al. J. Peds, 106:522, 1985) utilizing child length and stature data published by the CDC. * Females of Childbearing potential: Must have negative serum pregnancy test during screening and be neither breastfeeding nor intending to become pregnant during study participation. Females of childbearing potential must agree to avoid pregnancy during the study and agree to the use of 2 effective contraceptive