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 methods (hormonal and barrier method of birth control) prior to study entry, for the duration of study participation, and in the following 1 month after discontinuation of study treatment. Men with partner(s) of childbearing potential must take appropriate precautions to avoid fathering a child from screening until 6 months after discontinuation of study treatment and to use appropriate barrier contraception or abstinence. * Ability to comply with outpatient visits, laboratory testing, and study procedures during study participation * The patient, parent or guardian must voluntarily sign and date an informed consent approved (in addition to pediatric assent, if required) by an Independent Ethics Committee (IEC)/Institutional Review Board (IRB), prior to the initiation of any screening or study specific procedures. * Age: * Phase 1 (Part A): ≤ 30 years old (age at C1D1) * Phase 1 (Part B): \< 12 years old (age at C1D1) * Phase 2: ≤ 30 years old (age at C1D1) * Disease: * Phase 1: Pediatric patients with relapsed/refractory solid tumors (including primary CNS tumors). Patients with ALK, ROS1, or NTRK1/2/3 fusions are permitted to enroll in this cohort if progressed on prior targeted therapy or are not eligible for a higher priority study of single agent inhibition (ex: repotrectinib monotherapy IRB#20-077). Patients with tumors not characterized by any ALK/ROS/NTRK aberration are also permitted to enroll in this cohort. * Phase 2 * Cohort 1: Patients with molecularly defined desmoplastic small round cell tumor (DSRCT) * Cohort 2: Exploratory cohort of patients with relapsed or refractory solid tumors including CNS tumors (no requirement of ALK, ROS1, NTRK1-3 aberrations). Patients with ALK, ROS1, or NTRK1/2/3 fusions are permitted to enroll in this cohort if progressed on prior targeted therapy or are not eligible for a higher priority study of single agent inhibition (ex: repotrectinib monotherapy IRB# 20-077). Note: Refractory disease is defined as the presence of persistent abnormality on conventional MRI imaging that is further distinguished by histology (biopsy or sample of lesion) or advanced imaging, OR as determined by the treating physician and discussed with the primary investigator prior to enrollment. * Cohort 3: Patients with recurrent or progressive DIPG. Patients with typical DIPG, defined as tumors with a pontine epicenter and diffuse involvement of at least 2/3 of the pons on at least 1 axial T2-weighted image, are eligible. No histologic confirmation is required. Patients with pontine tumors that do not meet radiographic criteria for typical DIPG (e.g., focal tumors or those involving less than 2/3 of the pontine cross sectional area with or without extrapontine extension) are eligible if the tumors are biopsied and proven to be high-grade gliomas (such as anaplastic astrocytoma, glioblastoma, high-grade glioma NOS, and/or H3 K27M-mutant by immunohistochemistry or next generation sequencing CLIA certified) by institutional diagnosis. * Patients treated in Phase 1 at RP2D will be evaluable in the Phase 2 cohort if they meet all other inclusion criteria for the specified cohort. Patients receiving oral capsule OR oral suspension can be included in Phase 2 cohort. Enrollment of patients of at least 12 years old can begin treatment in Phase 2 once TPX-0005 (Repotrectinib) combination therapy RP2D is defined in Phase 1A (even if Phase 1B is not yet completed) Exception: DIPG patients may be enrolled on phase 2 cohort 3 prior to the completion of Phase 1 including the Phase 1 part B (PK expansion) since they will receive TPX-0005 (Repotrectinib) monotherapy at the pediatric RP2D. * Tissue Analysis * Phase 1: All patients must have archived tissue available for analysis (exception: DIPG patients), but ALK/ROS/NTRK status verification is not required prior to enrollment. If no archival tissue is available, waiver may be permitted by study PI (phase 1 only). * Phase 2: Prior to enrollment, all patients must have ALK/ROS/NTRK status evaluated in CLIA lab or equivalent by any nucleic acid-based diagnostic testing method (e.g., next-generation sequencing \[NGS\], Sanger sequencing, reverse transcription-polymerase chain reaction). Exception: Patients with molecularly defined DSRCT do not require ALK/ROS/NTRK status confirmed prior to enrollment. Exception: Patients enrolling on cohort 3 (recurrent/progressive DIPG) Exclusion Criteria: * Phase 1- patients with known bone marrow disease * Concurrent participation in another therapeutic clinical trial * Major surgery within 14 days (2 weeks) prior to C1D1. Central venous access (Broviac, MediPort) placement does not meet criteria for major surgery. * Pregnancy or lactation * Known active systemic infections requiring ongoing treatment (bacterial, fungal, viral including human immunodeficiency virus positivity). Skin or other superficial infections requiring topical treatment only are not an exclusion. * Gastrointestinal disease (e.g., Crohn's disease, ulcerative colitis, short gut syndrome) or other malabsorption syndromes that would impact on drug absorption. * Peripheral neuropathy CTCAE grade ≥ 3. * Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or that may interfere with the interpretation of study results and, in the judgment of the Investigator, would make the subject inappropriate for entry into this study, or could compromise protocol objectives in the opinion of the Investigator and/or Turning Point Therapeutics. * Current use or anticipated need for drugs that are known to be strong CYP3A4 inhibitors or inducers * Disease progression while on treatment with irinotecan/temozolomide. * Gilbert Syndrome or Crigler-Najjar * Prolonged QTc: 450m/s for male patients and 470ms for female patients.