Tivozanib As Maintenance Therapy In GYN

Once the participant has signed the consent form, they will be asked to undergo some screening tests or procedures to find out if the participant can be in the research study. Many of these tests and procedures are likely to be part of regular cancer care and may be done even if it turns out that the participant do not take part in the research study. If the participant has had some of these tests or procedures recently, they may or may not have to be repeated. * A medical history, which includes questions about the participant's health, current medications, and any allergies. * Performance status, which evaluates how the participant is able to carry on with their usual activities. * A tumor assessment by CT (Computerized Tomography) scan or MRI (Magnetic Resonance Imaging. * Blood tests. * Urine test. * Electrocardiogram (ECG) If these tests show that the participant is eligible to participate in the research study, the participant will begin the study treatment. If the participant does not meet the eligibility criteria, the participant will not be able to participate in this research study. Additional research procedures to be performed during this study: \- Archival tumor testing: During this study, additional tests will be performed on a sample of the participant's original tumor that has been stored in the institution's tissue banks. These tests will be performed on tumor tissue samples from previous biopsies or surgeries for the participant's cancer. The research done on these samples will involve looking at DNA and proteins in the participant's cancer to see if researchers can learn more about the participant's type of cancer and understand how tivozanib might work on their tumor. Testing of this sample will not require the participant to undergo any additional research procedures. This research sample collection is a required part of this research study. Tissue collection / Ownership: Participation in this protocol involves providing specimen(s) of participant's tissue. Please know that if the investigator leaves the institution, the research and the tissue might remain at the DF/HCC or might be transferred to another institution. After the screening procedures confirm that the participant are eligible to participate in the research study: If the participant takes part in this research study, the participant will be randomized to receive tivozanib by mouth or no therapy. The participant will be given a study drug diary for each treatment if the participant is randomized to the tivozanib group. Each treatment cycle lasts 28 days (4 weeks). For participants who are randomized to receive tivozanib, the participant will be taking the study drug once per day for 3 weeks followed by a week of rest. The diary will also include special instructions for taking the study drug. The study drug will be taken once a day with plenty of water.