Tivozanib in Recurrent, Platinum-Resistant Ovarian, Fallopian Tube or Primary Peritoneal Cancer

Inclusion Criteria: * • Patients must have recurrent or persistent, platinum resistant epithelial ovarian, fallopian tube or primary peritoneal carcinoma; platinum-resistant disease is defined as a recurrence within 6 months of completing adjuvant, platinum-based chemotherapy * Patients must have measurable disease or non-measurable (detectable) disease: * Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be greater than or equal to 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or by clinical exam; or greater than or equal to 20 mm when measured by chest x-ray; lymph nodes must be greater than or equal to 15 mm in short axis when measured by CT or MRI * Non-measurable (detectable) disease in a patient is defined in this protocol as one who does not have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) criteria but does have a cancer antigen 125 (CA-125) greater than or equal to two times the upper normal limit within the last 60 days (confirmatory at baseline) and at least one of the following conditions: * Ascites and/or pleural effusion attributed to tumor * Hypermetabolic lesions on positron emission tomography (PET) scan * Patients with measurable disease must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Recovery from effects of recent surgery, radiotherapy, or chemotherapy: * Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\]) * Any other prior therapy directed at the malignant tumor, including chemotherapy, biological/targeted (non-cytotoxic) agents and immunologic agents, must be discontinued at least three weeks prior to registration * At least 4 weeks must have elapsed since the patient underwent any major surgery (e.g., major: laparotomy, laparoscopy, thoracotomy, video assisted thorascopic surgery (VATS); there is no restriction on minor procedures (e.g., minor: central venous access catheter placement, ureteral stent placement or exchange, paracentesis, thoracentesis) * Patients must have had one prior taxane and platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organo platinum compound; this initial treatment may have included intraperitoneal therapy, consolidation, non-cytotoxic (biologic/targeted agents, such as bevacizumab) or extended therapy administered after surgical or non-surgical assessment; there is no maximum number of prior regimens; * patients may not have had any prior systemic therapy (including interleukin-2, interferon-alpha, chemotherapy, bevacizumab, investigational or licensed drug that targets vascular endothelial growth factor \[VEGF\] or VEGF receptors/pathway or are mammalian target of rapamycin \[mTOR\] inhibitors) for treatment of recurrent ovarian cancer * Patients must have signed an approved informed consent and authorization permitting the release of personal health information * Patients must meet pre-entry requirements * A female is eligible to participate if she is of non-childbearing potential or as documentation of a negative pregnancy test prior to the start of the study treatment; sexually active pre-menopausal female subjects must agree to use adequate, highly effective contraceptive measures, while on study and for 45 days after the last dose of last study drug; effective birth control includes (a) intrauterine device (IUD) plus one barrier method; (b) oral, implantable or injectable contraceptives plus one barrier method; or (c) 2 barrier methods; effective barrier methods are male or female condoms, diaphragms, and spermicides (creams or gels that contain a chemical to kill sperm) Exclusion Criteria: * • Age \< 18 years * Patients who have had previous treatment with tivozanib * Hemoglobin \< 9.0 g/dL * Absolute neutrophil count (ANC) \< 1500 per mm\^3 * Platelet count \< 100,000 per mm\^3 * Total bilirubin \> 1.5 × upper limit of normal (ULN) (or \> 2.5 x ULN for subjects with asymptomatic Gilbert's syndrome) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 × ULN (or \> 5 × ULN for subjects with liver metastasis) * BOTH total bilirubin \> ULN AND AST/ALT \> ULN * Alkaline phosphatase \> 2.5 × ULN (or \> 5 × ULN for subjects with liver or bone metastasis) * Creatinine \> 2.0 × ULN * Prothrombin time (PT) such that international normalized ratio (INR) \> 1.5 x ULN (unless a patient is on therapeutic warfarin) or a partial thromboplastin time (PTT) \> 1.5 x ULN * Proteinuria \> 3+ by urinalysis or urine dipstick * Significant cardiovascular disease, including: * Symptomatic left ventricular dysfunction or baseline left ventricular ejection fraction (LVEF) by multigated acquisition scan (MUGA) or echocardiogram (ECHO) of =\< lower limit of institutional normal (LLN) * Uncontrolled hypertension: systolic blood pressure of \> 140 mmHg or diastolic blood pressure of \> 90 mmHg documented on 2 consecutive measurements taken at least 24 hours apart * Myocardial infarction, severe angina, or unstable angina within 6 months prior to administration of first dose of study drug * History of serious ventricular arrhythmia (i.e., ventricular tachycardia or ventricular fibrillation) * Cardiac arrhythmias requiring anti-arrhythmic medications (except for atrial fibrillation that is well controlled with anti-arrhythmic medication) * Coronary or peripheral artery bypass graft within 6 months of screening * History of class III or IV congestive heart failure, as defined by the New York Heart Association * Central nervous system metastases; Note: subjects with previously treated (radiotherapy or surgery) brain metastasis that have been stable without steroid treatment for at least 3 months following prior treatment may be enrolled * Non-healing wound, bone fracture, or skin ulcer * Active peptic ulcer disease, inflammatory bowel disease, ulcerative colitis, or other gastrointestinal condition with increased risk of perforation; history of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 4 weeks prior to administration of first dose of study drug * Serious/active infection or infection requiring parenteral antibiotics * Corrected QT interval (QTc) of \> 480 msec using Bazett's formula * Radiotherapy or minor surgical procedure within 2 weeks, or major surgical procedure within 4 weeks prior to administration of first dose of study drug; inadequate recovery from prior surgical procedure * Significant thromboembolic or vascular disorders within 6 months prior to administration of first dose of study drug, including but not limited to: * Deep vein thrombosis * Pulmonary embolism * Cerebrovascular accident (CVA) or transient ischemic attack (TIA) * Peripheral arterial ischemia \> grade 2 (per National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version 4.0) * Significant bleeding disorders within 6 months prior to administration of first dose of study drug, including but not limited to: * Hematemesis, hematochezia, melena or other gastrointestinal bleeding \>= grade 2 (per CTCAE version 4.0) * Hemoptysis or other pulmonary bleeding \>= grade 2 (per CTCAE Version 4.0) * Hematuria or other genitourinary bleeding \>= grade 2 (per CTCAE Version 4.0) * Currently active second primary malignancy, including hematologic malignancies (leukemia, lymphoma, multiple myeloma, etc.), other than non-melanoma skin cancers, non-metastatic prostate cancer, in situ cervical cancer, and ductal or lobular carcinoma in situ of the breast; subjects are considered to have a currently active malignancy if they have completed anti-cancer therapy and have not been disease free for \> 2 years * Pregnant or lactating females * History of genetic or acquired immune suppression disease such as human immunodeficiency virus (HIV); subjects on immune suppressive therapy for organ transplant * Life-threatening illness or organ system dysfunction compromising safety evaluation * Requirement for hemodialysis or peritoneal dialysis * Inability to swallow capsules, malabsorption syndrome or gastrointestinal disease that severely affects the absorption of study drugs, major resection of the stomach or small bowel, or gastric bypass procedure * Known hypersensitivity to drugs chemically related to tivozanib hydrochloride or sunitinib or their excipients * Psychiatric disorder or altered mental status precluding informed consent or protocol-related testing