Silmitasertib (CX-4945) in Combination With Chemotherapy for Relapsed Refractory Solid Tumors

The purpose of this study is to evaluate the investigational drug, silmitasertib (a pill taken by mouth), in combination with FDA approved drugs for solid tumors. An investigational drug is one that has not been approved by the U.S. Food \& Drug Administration (FDA), or any other regulatory authorities around the world for use alone or in combination with any drug, for the condition or illness it is being used to treat. The goals of this part of the study are: * Establish a recommended dose of silmitasertib in combination with chemotherapy * Test the safety and tolerability of silmitasertib in combination with chemotherapy in subjects with cancer * To determine the activity of study treatments chosen based on: * How each subject responds to the study treatment * How long a subject lives without their disease returning/progressing

Inclusion Criteria: 1. Age: Less than 30 years old at initial diagnosis 2. Pathology All subjects must have a confirmed diagnosis of tumor type. Phase I: Relapsed/refractory solid tumors: Neuroblastoma, Ewing Sarcoma, Osteosarcoma, Rhabdomyosarcoma, Liposarcoma Phase II: * Relapsed/refractory Neuroblastoma * Relapsed/refractory Ewing sarcoma 3. Tumor assessment: Disease assessment is required for eligibility and must be done after last dose of previous therapy and prior to first dose of study drug. 4. Disease Status: Relapsed/Refractory Neuroblastoma Relapsed disease defined as neuroblastoma that was previously in remission after standard therapy (at least 4 cycles of aggressive multi-drug induction chemotherapy, with or without radiation and surgery, followed by immunotherapy, or according to a standard high-risk treatment/neuroblastoma protocol) and has now relapsed and is in any number of relapses. Refractory disease defined as High-risk neuroblastoma (as defined by INRG) that failed to achieve CR after at least 4 cycles of aggressive multi-drug induction chemotherapy, progression during upfront therapy or with disease remaining after standard immunotherapy. International Neuroblastoma Risk Group Staging System (INRG) High Risk NB defined as one of the following: 1. Any age with International Neuroblastoma Risk Group (INRG) Stage L2, MS, or M with MYCN amplification 2. Age ≥ 547 days and INRG Stage M regardless of biologic features 3. Any age initially diagnosed with INRG Stage L1 MYCN amplified NBL who have progressed to Stage M without systemic chemotherapy 4. Age ≥ 547 days of age initially diagnosed with INRG Stage L1, L2, or MS who have progressed to Stage M without systemic chemotherapy Relapsed/refractory Sarcoma Subjects that have relapsed following standard of care therapy or having progressed during standard of care therapy. Standard of care therapy for sarcoma includes multi-agent chemotherapy with local control consisting of either surgery or radiation therapy. 5. Measurable or evaluable disease, including at least one of the following: * Measurable tumor by CT or MRI * MIBG or PET that is positive for disease * Bone Marrow biopsy/aspirate that is positive for disease 6. Timing from prior therapy: Subjects must have fully recovered from the acute toxic effects of all prior anti- cancer therapy and be within the following timelines: 1. Myelosuppressive chemotherapy: Must not have received within 2 weeks of enrollment onto this study. 2. Small Molecule Inhibitors (anti-neoplastic agent): At least 2 weeks from the completion of therapy with a small molecule inhibitor. 3. Immunotherapy: At least 4 weeks since the completion of any type of immunotherapy, e.g. tumor vaccines, CAR-T cells, anti-GD2 Monoclonal antibodies (ex. naxitamab, dinutuximab, etc.). 4. Radiotherapy: At least 30 days since the last treatment except for radiation delivered with palliative intent to a non-target site. 5. Stem Cell Transplant: * Allogeneic: No evidence of active graft vs. host disease * Allogeneic/Autologous: ≥ 2 months must have elapsed since transplant. 6. MIBG Therapy: At least 6 weeks since treatment with MIBG therapy. 7. Subjects must have a Lansky or Karnofsky Performance Scale score of \>/= 50. 8. Subjects must have adequate organ function at the time of enrollment: * Cardiac: Subjects must have a QTcF ≤ 480 msc. * Hematological: Hematological recovery as defined by ANC ≥750/μL * Liver: Adequate liver function as defined by AST and ALT \