A Non-Randomized, Open-label Phase II Trial Testing the Activity of XL092 (Zanzalintinib) in Patients With Advanced Leiomyosarcoma, Bone Sarcoma or Translocation-associated Soft Tissue Sarcoma

Inclusion Criteria For Cohort 1 - Leiomyosarcoma: * Patients must have histologically confirmed leiomyosarcoma that has been clinically determined to be metastatic or unresectable. Pathology must have been reviewed at a National Comprehensive Cancer Network (NCCN) designated cancer center such as Northwestern University's Lurie Cancer Center. * Patients must have undergone at least 2 or more lines of antineoplastic treatment, but no more than 2 lines of treatment can be a tyrosine kinase inhibitor (TKI). Inclusion Criteria For Cohort 2 - Bone Sarcoma: * Patients must have histologically confirmed diagnosis of metastatic or unresectable bone sarcoma. Pathology must have been reviewed at a National Comprehensive Cancer Network (NCCN) designated cancer center such as Northwestern University's Lurie Cancer Center. * Patients must have undergone at least 1 line of antineoplastic treatment, but no more than 2 lines of treatment can be a tyrosine kinase inhibitor (TKI). Inclusion Criteria For Cohort 3 - Translocation-associated Soft Tissue Sarcoma: * Patients must have histologically confirmed diagnosis of metastatic or unresectable translocation-associated soft tissue sarcoma (TAS). Pathology must have been reviewed at a National Comprehensive Cancer Network (NCCN) designated cancer center such as Northwestern University's Lurie Cancer Center. * Patients must have undergone greater than 2 lines of antineoplastic treatment, but no more than 2 lines of treatment can be a tyrosine kinase inhibitor (TKI). Inclusion Criteria for All Cohorts/Sarcoma Types * Patients must have measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1. * Patients must be aged ≥ 18 years on day of signing any informed consent documents. * Patients must exhibit a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale or \> 70% on the Karnofsky Scale. * Absolute neutrophil count (ANC) ≥ 1,500/mcL (without granulocyte colony-stimulating factor support within 21 days of screening sample collection) * Hemoglobin (Hgb) ≥ 9 g/dL without transfusion within 21 days of screening laboratory sample collection * Platelets (PLT) ≥ 100,000/mm\^3 (\> 100 GI/L) without transfusion within 21 days of screening laboratory sample collection * International normalized ratio (INR) ≤ 1.5 ULN and activated partial thromboplastin time (aPTT) ≤ 1.2 x upper limit of normal (ULN) * Total bilirubin ≤ 1.5 x institutional upper limit of normal ULN; for patients with Gilbert's disease, total bilirubin ≤ 3 x ULN * Alanine aminotransferase (AST) ≤ 3 x institutional ULN * Aspartate aminotransferase (ALT) ≤ 3 x institutional ULN * Alkaline phosphatase (ALP) ≤ 3 x institutional ULN; for patients with documented bone metastasis, ALP ≤ 5 x ULN * Serum creatinine ≤ 1.5 x institutional ULN OR calculated creatinine clearance ≥ 40 mL/min ( ≥ 0.67 mL/sec) using the Cockcroft-Gault equation * Creatinine clearance ≥ 40mL/min * Urine protein-to-creatinine ratio (UPCR) ≤ 1 mg/mg ( ≤ 113.12 mg/mmol) * Patient of child-bearing potential (POCBP) and any of their partners with sperm-producing reproductive capability must agree to use a highly effective method of contraception throughout the course of the study and for 186 days after the last dose of treatment. Additional contraceptive method, such as a barrier method (e.g., condom) is also required * Patients with sperm-producing reproductive capacity (PWSPRC) treated or enrolled on this protocol must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence), with partners of childbearing potential from time of informed consent, for the duration of study participation, and for 96 days following completion of therapy * Patients must have ejection fraction \> 50% by either MUGA scan or echocardiogram. * Patients must be capable of understanding and complying with the protocol requirements. * Patients must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients who have received previous treatment with XL092. * Patients who have received any type of small-molecule kinase inhibitor (including an investigational kinase inhibitor) within 14 days prior to study day 1 treatment. * Patients who have received \> 2 prior tyrosine kinase inhibitor therapies as anticancer treatments. * Patients who have had prior chemotherapy, or radiation therapy within 4 weeks prior to start of study treatment unless they have recovered from their prior therapy (toxicity and/or complications) such that they now meet all other eligibility criteria * Patients who have received radiation therapy for bone metastasis within 14 days prior to registration * Patients who have undergone systemic treatment with radionuclides within 6 weeks (42 days) before first dose of study treatment * Patients with clinically relevant complications from prior radiation therapy requiring ongoing therapy, per the opinion of the treating investigator enrolling the patient. * Patients with a known prior or concurrent malignancy that is progressing or requires active treatment within 2 years of first dose of study treatment. Note: The following exceptions may be made: * For patients with malignancies like basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer; or superficial skin cancers, localized low-grade tumors deemed cured and not treated with systemic therapy, and incidentally diagnosed prostate cancer if assessed as stage ≤ T2N0M0 and Gleason score ≤ 6. * For patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen. * Patients with known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to first dose of study treatment. Note: Base of skull lesions without definitive evidence of dural or brain parenchymal involvement are allowed. Note: Eligible patients must be neurologically asymptomatic and without corticosteroid treatment at the time of first dose of study treatment. * Patients who are on concomitant anticoagulation therapy with oral anticoagulants (e.g., warfarin or direct thrombin and factor Xa inhibitors) and platelet inhibitors (e.g., clopidogrel). Note: Allowed anticoagulants are low-dose aspirin for cardioprotection (per local applicable guidelines) and low molecular weight heparins (LMWH). Therapeutic doses of LMWH are not permitted in patients with brain metastases. Note: Patients must have discontinued oral anticoagulants within 3 days or 5 half-lives prior to first study treatment, whichever is longer. * Patients who are taking any complementary medications (e.g., herbal supplements or traditional Chinese medicines) to treat the disease under study within 2 weeks (14 days) prior to start of treatment. Note: taking complementary medications to treat symptoms of the cancer is allowed. * The patient has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias (e.g., ventricular flutter, ventricular fibrillation, Torsades de pointes) * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic of \> 90 mm Hg diastolic despite optimal antihypertensive treatment * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction, or other clinically significant ischemic events within 12 months prior to first dose of study treatment. Note: Patients who did not require prior anticoagulant therapy may be eligible must be discussed and approved by the principal investigator (PI) * Pulmonary embolism (PE) or deep vein thrombosis (DVT) or prior clinically significant venous or non-cerebrovascular accident (CVA)/TIA arterial thromboembolic events within 6 months before to first dose of study treatment. * Prior history of myocarditis * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: * Tumors invading the GI tract from external viscera * Active peptic ulcer disease, inflammatory bowel disease, diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, or acute pancreatitis * Abdominal fistula, gastrointestinal perforation, bowel obstruction, or intra-abdominal abscess must be confirmed prior to first dose of study treatment * Known gastric or esophageal varices * Acute obstruction of the bowel, gastric outlet, or pancreatic or biliary duct within 6 months unless cause of obstruction is definitively managed and subject is asymptomatic * Patients with clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 mL) of red blood, or other history of significant bleeding (e.g., pulmonary hemorrhage) within 84 days prior to registration. * Symptomatic cavitating pulmonary lesions or endobronchial disease (asymptomatic or radiated lesions allowed). * Lesions invading major blood vessel including but not limited to inferior vena cava, pulmonary artery, or aorta. Note: Patients with intravascular tumor extension (e.g., tumor thrombus in renal vein or inferior vena cava) may be eligible following PI approval * Patients who are capable of donating eggs for the purpose of reproduction must not do so throughout the course of the study and for 186 days after the last dose of treatment * Patients who are capable of donating sperm for the purpose of reproduction must not do so throughout the course of the study and for 96 days after the last dose of treatment * Other clinically significant disorders that would preclude safe study participation, including, but not limited to: * Active infection requiring systemic treatment. Note: This criterion applies only at enrollment; if a patient develops an infection while on study treatment, they may continue to receive study treatment. Note: prophylactic antibiotic treatment is allowed * Known infection with acute or chronic hepatitis B or C, known human immunodeficiency virus (HIV), or acquired immunodeficiency syndrome (AIDS)-related illness * Known positive test for or suspected infection with SARS-CoV-2 within one month prior to enrollment. Note: Demonstration that the patient has fully recovered from the infection is required to be eligible for enrollment * Serious non-healing wound/ulcer/bone fracture. Note: non-healing wounds or ulcers are permitted if they are due to tumor-associated skin lesions * Malabsorption syndrome * Pharmacologically uncompensated, symptomatic hypothyroidism * Moderate to severe hepatic impairment (Child-Pugh B or C) * Requirement for hemodialysis or peritoneal dialysis * History of solid organ or allogenic stem cell transplant * Recent surgery within the following parameters: * Major surgery (e.g., GI surgery or removal/biopsy of brain metastasis) within 8 weeks prior to study treatment * Minor surgery (e.g., simple excision, tooth extraction) within 5 days prior to first dose of study treatment. Note: if a patient has had a recent surgery outside of the proscribed interval, complete wound healing from said surgery must have occurred prior to first dose of study treatment. Note: Fresh tumor biopsies should be performed at least 5 days prior to registration. Patients with clinically relevant ongoing complications from prior surgical procedures, including biopsies, are not eligible * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 480 ms within 14 days per electrocardiogram (ECG) prior to first dose of study treatment Note: Triplicate ECG evaluations will be performed and the average of these 3 consecutive results for QTcF will be used to determine eligibility * Patients with any unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria for Adverse Event (CTCAE) grade \> 1 at baseline from a previous anticancer therapy, with the following exceptions: * Alopecia, vitiligo, and the laboratory values * Patients with grade ≥ 2 neuropathy will be evaluated on a case-by-case basis after consultation with the treating physician * Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with XL092 may be included only after consultation with the principal investigator * Patients who have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to XL092 * Patients who are pregnant (positive serum or urine test within 72 hours prior to enrollment) or nursing. Pregnant people are excluded from this study because XL092 is a next-generation tyrosine kinase inhibitor with potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the nursing parent with XL092, breastfeeding should be discontinued if the nursing parent is treated with XL092. Note: If a urine pregnancy test is positive or cannot be confirmed negative, a serum pregnancy test will be required * Patients with psychiatric illness/social situations that would limit compliance with study requirements, per the opinion of the treating investigator * XL092 is administrated orally; patients who are unable to swallow, retain, and/or absorb pills are not eligible for this study * Patients who are currently participating in or have participated in a study of an investigational agent or have used an investigational device within 4 weeks prior to the first dose of treatment * Other conditions which, in the opinion of the Investigator, would compromise the safety of the patient or the patient's ability to complete the study