Testing the Addition of an Anti-cancer Drug, DT2216, to the Usual Chemotherapy Treatment for Relapsed or Refractory Solid Tumors and Fibrolamellar Carcinoma

Inclusion Criteria: * PHASE 1: Patients between ≥ 1 year and ≤ 21 years of age at the time of study enrollment * PHASE 2: Patients between ≥ 1 year and ≤ 39 years of age at the time of study enrollment * PHASE 1: Patients with recurrent/refractory solid tumors excluding primary central nervous system tumors * PHASE 2: Patients with (FLC), which must include genomic confirmation of the DNAJB1:PRKACA fusion performed at a Clinical Laboratory Improvement Act (CLIA)-certified laboratory * PHASE 1: Patients must have either measurable or evaluable disease * PHASE 2: Patients must have measurable disease * PHASE 1: Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * PHASE 2: Patients must have FLC which is recurrent/refractory to at least one line of prior systemic therapy * Patients with FLC that is unresectable at initial diagnosis but is not recurrent/refractory to at least one prior line of systemic therapy nor metastatic are NOT eligible for either phase 1 or phase 2 * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients ≤ 16 years of age * Patients must have fully recovered (grade \< 2) from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy…