Testing the Addition of an Anti-Cancer Drug, Daraxonrasib, for Relapsed or Refractory Solid Tumors With RAS Mutations

Inclusion Criteria: * PARTS A1 AND B: Patients must be ≥ 2 years and ≤ 17 years of age at the time of study enrollment * PART A2: Patients must be ≥ 1 year and ≤ 17 years of age at the time of study enrollment * Patients with recurrent or refractory extracranial solid tumors. Patients must have had histologic verification of malignancy at original diagnosis or relapse * PARTS A1 AND A2: Patients with relapsed or refractory RAS mutant extracranial solid tumors * PARTS B1, B2, AND B3: Patients with relapsed or refractory fusion-negative rhabdomyosarcoma (B1: RMS), neuroblastoma (B2: NBL), or other extracranial solid tumors (B3: Other) * All patients must have a College of American Pathologists (CAP)/Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory report which documents RAS mutation at diagnosis or time of relapse, defined as nonsynonymous mutations in KRAS, NRAS, or HRAS at codons 12, 13, or 61 (G12, G13, or Q61) * PAST A: Patients must have either measurable or evaluable disease * PART B: Patients must have International Neuroblastoma Response Criteria (INRC) evaluable (neuroblastoma) or Response Evaluation Criteria in Solid Tumors (RECIST) measurable (all other diagnoses) disease * NEUROBLASTOMA: Bone marrow aspirates and biopsies are required at baseline for neuroblastoma patients, per INRC guidelines * SOLID TUMORS: Bone marrow aspirates and biopsies are required at baseline for patients with other solid tumors with a history of bone marrow metastatic disease * 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 * Karnofsky ≥ 50% for patients \>16 year of age and Lansky ≥ 50% for patients ≤ 16 years of age. Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. See https://www.cogmembers.org/site/pages/default.aspx?page=Prot\_reference\_ materials under Standard References * 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 prior to enrollment. If after the required timeframe, the numerical eligibility criteria are met, e.g., blood count criteria, the patient is considered to have recovered adequately. * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive: See DVL homepage on the Children's Oncology Group (COG) Members site for commercial and investigational agent classifications. For agents not listed, the duration of this interval must be discussed with the study chair and the study-assigned Research Coordinator prior to enrollment. * Solid Tumor Patients: ≥ 21 days after the last dose of myelosuppressive chemotherapy (42 days if prior nitrosourea). Please refer to the table of myelosuppressive/Anticancer Agents on the COG website: https://www.cogmembers.org/uploadedFiles/Site/Disc/DVL/Documents/TableOfMyelosuppressiveAnti-CancerAgents.pdf * Anti-cancer agents not known to be myelosuppressive (e.g., not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): ≥ 7 days after the last dose of agent. See the DVL homepage on the COG Members site for commercial and investigational agent classifications. For agents not listed, the duration of this interval must be discussed with the study chair and the study-assigned Research Coordinator prior to enrollment. * Antibodies: ≥ 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to Grade ≤ 1. * Corticosteroids: If used to modify immune adverse events related to prior therapy, ≥ 14 days must have elapsed since last dose of corticosteroid * Hematopoietic growth factors: ≥ 14 days after the last dose of a long-acting myeloid growth factor (e.g., pegfilgrastim) or 7 days for short acting myeloid growth factor or platelet growth factor/stimulating agents (e.g., romiplostim, eltrombopag). For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur. * Interleukins, Interferons and Cytokines (other than Hematopoietic Growth Factors): ≥ 21 days after the completion of interleukins, interferon or cytokines (other than Hematopoietic Growth Factors). * Stem cell Infusions (with or without total body irradiation \[TBI\]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: ≥ 84 days after infusion and no evidence of graft versus host disease (GVHD). * Autologous stem cell infusion including boost infusion: ≥ 42 days. * Cellular Therapy: ≥ 42 days after the completion of any type of cellular therapy (e.g., modified T cells, natural killer \[NK\] cells, dendritic cells, etc.). * Radiation (XRT)/External Beam Irradiation including Protons: ≥ 14 days after local XRT; ≥ 56 days from thoracic XRT; ≥ 150 days after TBI, craniospinal XRT or if radiation to ≥ 50% of the pelvis; ≥ 42 days if other substantial bone marrow (BM) radiation. * Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131I MIBG): ≥ 42 days after systemically administered radiopharmaceutical therapy. * Patients must not have received prior exposure to daraxonrasib or other direct RAS inhibitors (e.g., sotorasib, adagrasib) * Peripheral absolute neutrophil count (ANC) ≥ 1000/uL (for patients with solid tumors without known bone marrow involvement) * Platelet count ≥ 100,000/uL (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) (for patients with solid tumors without known bone marrow involvement) * Hemoglobin ≥ 8.0 g/dL at baseline (may receive red blood cell \[RBC\] transfusions) (for patients with solid tumors without known bone marrow involvement) * Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions). These patients will not be evaluable for hematologic toxicity. At least 5 of every cohort of 6 patients must be evaluable for hematologic toxicity for the dose escalation part of the study. If dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity * \* For patients ≤ 17 years old estimated glomerular filtration rate (GFR) (eGFR) ≥ 60 mL/min/1.73 m\^2 "Bedside" Schwartz formula (2009): eGFR = 0.413 x (height (cm) / serum creatinine (mg/dL)) An online calculator is available through the National Kidney Foundation at http://www.kidney.org/professionals/kdoqi/gfr\_calculatorped * For patients \> 17 years old the Cockroft-Gault equation should be utilized to calculate creatinine clearance * OR for any age group: * a 24 hour urine Creatinine clearance ≥ 60 mL/min/1.73 m\^2 * OR a GFR ≥ 60 mL/min/1.73 m\^2. GFR must be performed using direct measurement with a nuclear blood sampling method OR direct small molecule clearance method (iothalamate or other molecule per institutional standard). Cystatin C based methods for estimation of GFR are not acceptable * Bilirubin (total or sum of conjugated + unconjugated) ≤ 1.5 x upper limit of normal (ULN) for age except in patients diagnosed with Gilbert's disease for which bilirubin must be ≤ 3.0 × ULN * Alanine aminotransferase (ALT) ≤ 3 x ULN, unless attributed to tumor involvement then ALT ≤ 5 x ULN * Aspartate aminotransferase (AST) ≤ 3 x ULN, unless attributed to tumor involvement then AST ≤ 5 x ULN * Serum albumin ≥ 2 g/dL * International normalization ratio (INR) ≤ 1.5 * Corrected QT (QTc) ≤ 480 ms * Anti-cancer agents: Patients who are currently receiving other anti-cancer agents are not eligible Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study because there is yet no available information regarding human fetal or teratogenic toxicities. Pregnancy tests must be obtained in girls who are post-menarchal. Males or females of reproductive potential may not participate unless they have agreed to use two effective methods of birth control, including a medically accepted barrier or contraceptive method (e.g., male or female condom) for the duration of the study and for at least one month after the last dose of study treatment for females and one week after the last dose of study treatment for males. Abstinence is an acceptable method of birth control * Corticosteroids: Patients must be on a stable or decreasing dose of corticosteroids for at least 7 days prior to enrollment. If used to modify immune adverse events related to prior therapy, ≥ 14 days must have elapsed since last dose of corticosteroid * Investigational drugs: Patients who are currently receiving another investigational drug are not eligible * Anti-GVHD agents post-transplant: Patients must not be receiving tacrolimus or other medications to prevent graft-versus-host disease post bone marrow transplant * Cyclosporine and derivatives: Patients must not require concomitant treatment with systemically bioavailable cyclosporine A or its derivatives * CYP3A4 inhibitors/inducers: Moderate or strong systemic CYP3A4 inhibitors or inducers are prohibited during treatment with daraxonrasib. These agents should be discontinued at least 14 days prior to enrollment. * Local or topical treatments are allowed. * Seville oranges, grapefruit, and grapefruit products are considered moderate or strong CYP3A4 inhibitors on this protocol * Patients enrolled on Parts A1 and B must be able to swallow 20 mg and 100 mg tablets intact. Nasogastric or G tube administration is not allowed * Patients whose tumors harbor a somatic PAX3 or FOXO1 translocation found on deoxyribonucleic acid (DNA), ribonucleic acid (RNA), or fluorescence in situ hybridization (FISH) testing are ineligible * Patients with primary central nervous system (CNS) tumors or untreated CNS metastases are ineligible. * Treated CNS metastases are not excluded if stable and asymptomatic. * All patients with previously treated brain metastases must have a magnetic resonance imaging (MRI), or computed tomography (CT) if MRI is contraindicated, of the brain within 28 days prior enrollment to confirm there has been no disease progression * Patients with any condition expected to interfere with the absorption of orally administered medications are ineligible * Patients who have acute coronary syndrome (e.g., unstable angina, myocardial infarction) within 6 months prior to study enrollment * Patients who have significant cardiovascular disease (such as New York Heart Association Class II to IV congestive heart failure) within 1 month prior to study enrollment * Patients with who have a history of interstitial lung disease (ILD) or non-infectious pneumonitis requiring high-dose glucocorticoids or any active ILD or pneumonitis, or prior thoracic radiotherapy within 8 weeks of enrollment * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of enrollment are eligible * Patients with known hepatitis B or C with detectable viral load are not eligible * Patients who have had major surgery ≤ 28 days prior to enrollment are not eligible * Patients who have an uncontrolled infection are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible