A Study to Test the Addition of the Drug Cabozantinib to Chemotherapy in Patients With Newly Diagnosed Osteosarcoma

Inclusion Criteria: * Patients must be \< 40 years of age at the time of enrollment. * Patients must have a body surface area of \>= 0.8 m\^2 at the time of enrollment. * Patients must have histologic diagnosis (by institutional pathologist) of newly diagnosed high grade osteosarcoma. Primary tumors of all extremity and axial sites are eligible as long as diagnosis of high-grade osteosarcoma is established. Osteosarcoma as a second malignancy is eligible if no prior exposure to systemic chemotherapies. * Feasibility Phase (NOTE: as of Amendment #2B, the feasibility phase has been completed) Patients must have metastatic disease and a resectable primary tumor. Designation of a primary tumor as resectable will be determined at the time of diagnosis by the institutional multidisciplinary team. For this study, metastatic disease is defined as one or more of the following: * Lesions which are discontinuous from the primary tumor, are not regional lymph nodes, and do not share a bone or body cavity with the primary tumor. Skip lesions in the same bone as the primary tumor do not constitute metastatic disease. Skip lesions in an adjacent bone are considered bone metastases. * Lung metastases: defined as biopsy-proven metastasis or the presence of one or more pulmonary lesions \>= 5 mm, OR multiple pulmonary lesions \>= 3 mm or greater in size. * Bone metastases: Areas suspicious for bone metastasis based on fludeoxyglucose F-18 (18F-FDG)-positron emission tomography (PET) scan (o…