This phase II trial studies how well cabozantinib-s-malate works in treating patients with ovarian, fallopian tube, or primary peritoneal cavity cancer that has come back or is growing, spreading, or getting worse. Cabozantinib-s-malate may stop the growth of tumor cells by blocking the growth of new blood vessels necessary for tumor growth and also by blocking some of the enzymes needed for cell growth.

PRIMARY OBJECTIVES: I. To evaluate the anti-tumor activity of cabozantinib (XL184) (cabozantinib-s-malate) in women with persistent or recurrent clear cell ovarian cancer, based on the proportion of patients who survive progression-free for at least 6 months and the proportion who have objective tumor response (complete or partial). SECONDARY OBJECTIVES: I. To determine the nature, frequency and maximum degree of toxicity as assessed by Common Terminology Criteria for Adverse Events (CTCAE) version (v)4 for cabozantinib (XL184). II. To determine the progression free survival (PFS) and overall survival (OS) for patients with persistent or recurrent clear cell ovarian cancer treated with cabozantinib (XL184). TERTIARY OBJECTIVES: I. To examine the expression of phosphatase and tensin homolog gene (PTEN), phosphorylated v-akt murine thymoma viral oncogene homolog 1 (pAKT), cyclin E, and met proto-oncogene (MET) in formalin-fixed, paraffin-embedded tumor. II. To examine MET amplification (fluorescence in situ hybridization) in tumor specimens and the relationship to response. OUTLINE: Patients receive cabozantinib-s-malate orally (PO) once daily (QD) on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for 2 years, every 6 months for 3 years, and then annually thereafter.