Patient description: The patient is a 37-year-old woman who came to the clinic for a routine Pap smear. The test revealed stage 1B of cervical cancer. The patient tested positive for HPV 16. She has three sexual partners and four children. She underwent tubal ligation. She smokes 30 packs/year and drinks alcohol frequently. She is otherwise healthy. She was offered a radical hysterectomy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Anatomic Stage IV Breast Cancer AJCC v8 Clinical Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8 Clinical Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8 Clinical Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8 Locally Advanced Malignant Solid Neoplasm Locally Advanced Melanoma Locally Advanced Primary Malignant Central Nervous System Neoplasm Locally Advanced Sarcoma Metastatic Malignant Solid Neoplasm Metastatic Melanoma Metastatic Primary Malignant Central Nervous System Neoplasm Metastatic Sarcoma Pathologic Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8 Postneoadjuvant Therapy Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8 Postneoadjuvant Therapy Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8 Postneoadjuvant Therapy Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8 Prognostic Stage IIIC Breast Cancer AJCC v8 Prognostic Stage IV Breast Cancer AJCC v8 Stage IIIC Colorectal Cancer AJCC v8 Stage IIIC Lung Cancer AJCC v8 Stage IV Colorectal Cancer AJCC v8 Stage IV Lung Cancer AJCC v8 Stage IVA Colorectal Cancer AJCC v8 Stage IVA Lung Cancer AJCC v8 Stage IVB Colorectal Cancer AJCC v8 Stage IVB Lung Cancer AJCC v8 Stage IVC Colorectal Cancer AJCC v8 The patient (or legally acceptable representative if applicable) provides written informed consent for the study >= 18 years of age on the day of informed consent signing Patient has a locally advanced or metastatic solid tumor and has progressed on appropriate standard therapy, has not shown clinically meaningful benefit to appropriate standard therapy, has no available standard therapy, or has declined appropriate standard therapy NOTE: Specific solid tumor types but are not limited to melanoma, breast cancer, lung cancer, gastroesophageal cancer, colorectal cancer, sarcoma, solid tumors not otherwise specified (NOS), and primary central nervous system (CNS) tumors. Patients with any other solid tumor type with the exception of gastrointestinal stromal tumor (GIST) will be eligible for enrollment in the study Measurable disease per the v1.1 or Response Assessment in Neuro-Oncology (RANO) as appropriate (for Cohorts 1 and 2 only). NOTE: Patients in Cohort 3 can have measurable or non-measurable disease Documented pathogenic CKIT activating mutation (Cohort 1) OR pathogenic activating mutation (Cohort 2) based on tissue-based next-generation sequencing (NGS) diagnostic test (Oncomine Comprehensive Assay [OCA] or FoundationOne CDx) OR plasma cfDNA-detected (Guardant360) pathogenic CKIT or activating mutation (for patients with measurable disease) or tissue or cfDNA-detected pathogenic CKIT or activating mutation (for patients with non-measurable disease; Cohort 3). Mutation pathogenicity will be verified by the MD Anderson Cancer Center (MDACC) Precision Oncology Decision Support (PODS) team Has available archival tissue for CKIT or mutation testing Lymphocyte count >= 500/uL (within 28 days of study treatment initiation) White blood cell count > 2,500/uL and < 15,000/uL (within 28 days of study treatment initiation) Absolute neutrophil count >= 1.5 x 10^9/L (without granulocyte colony-stimulating factor support within 2 weeks of laboratory test used to determine eligibility) (within 28 days of study treatment initiation)  Patients who have GIST Patients with tyrosine kinase inhibitor (TKI)-resistant CKIT mutation V654A or T670I Patient with meningeal carcinomatosis, leptomeningeal carcinomatosis, spinal cord compression, or symptomatic or unstable brain metastases. Note: Patients with stable brain metastases (defined as asymptomatic or no requirement for high-dose or increasing dose of systemic corticosteroids and without imminent need of radiation therapy) are eligible (including those with untreated brain metastases). If applicable, patients must have completed brain radiation therapy and recovered adequately from any associated toxicity and/or complications prior to assessment. For patients who have received prior radiation therapy, post-treatment magnetic resonance imaging (MRI) scan should show no increase in brain lesion size/volume History of documented congestive heart failure (New York Heart Association functional classification III-IV) or serious cardiac arrhythmias requiring treatment QT interval corrected using Fridericia's formula of > 470 msec Is currently participating or has participated in a study of an investigational agent or has used an investigational device within 2 weeks prior to study treatment initiation Prior anticancer chemotherapy, hormone therapy, immunotherapy, targeted therapy, radiation therapy, or surgery within 2 weeks prior to study treatment initiation NOTE: Patients must have recovered from all adverse events (AEs) due to previous therapies to =< grade 1 or baseline NOTE: If patient received major surgery, she/he must have recovered adequately from the toxicity and/or complications from the intervention prior to study treatment initiation Arterial thrombotic or embolic events within 6 months prior to study treatment initiation, or venous thrombotic events within 2 weeks prior to study treatment initiation