Ziv-aflibercept in Treating Patients With Locally Advanced, Unresectable, or Metastatic Gynecologic Soft Tissue Sarcoma

Inclusion Criteria: * Histologically/cytologically confirmed soft tissue sarcoma of gynecologic tract including 1 of the following subtypes: uterine leiomyosarcoma, malignant mixed mullerian tumor/carcinosarcoma, disease originating in ovary/fallopian tube allowed * Locally advanced/unresectable/metastatic disease * Previously treated disease must have radiographic/clinical evidence of PD * Measurable disease-at least 1 lesion in at least 1 dimension (longest diameter) as \>=20mm with conventional techniques or as \>=10mm with spiral CT scan * Indicator lesions may not have been previously treated with surgery/radiotherapy/radiofrequency ablation unless PD has been confirmed * ECOG PS 0-2 OR Karnofsky PS 60-100% * Life expectancy\>=3 months * WBC\>=3,000/mm\^3 * Absolute neutrophil count\>=1,500/mm\^3 * Platelet count\>=75,000/mm\^3 * Bilirubin=\<1.5xULN * AST and ALT=\<3xULN * INR=\<1.5 (unless on warfarin) * Creatinine=\<1.5xULN OR creatinine clearance\>=60 mL/min * Urine protein\<1+ by dipstick OR 24-hour urine protein\<500 mg OR urine protein:creatinine ratio\<1 * Not pregnant/nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥6 months after treatment - No other active malignancy within past 5 years except adequately treated cervical carcinoma in situ/nonmelanoma skin cancer * No known hypersensitivity to Chinese hamster ovary cell products/other recombinant human antibodies * No history of allergic reactions attributed to compounds of similar chemical/biological composition to study agents * No serious/nonhealing wound/ulcer/bone fracture * No abdominal fistula/gastrointestinal perforation/bowel obstruction/intraabdominal abscess within past 28 days * No significant traumatic injuries within past 28 days * No evidence of bleeding diathesis/coagulopathy * No uncontrolled intercurrent illness including but not limited to: Ongoing/active infection, psychiatric illness or social situations that would preclude study compliance * \<=2 prior cytotoxic chemotherapy regimen for recurrent, locally advanced or metastatic disease * Recovered from prior therapy * No prior antiangiogenic agent Exclusion Criteria: * \< 4weeks since prior chemotherapy (\<6 weeks for nitrosoureas/carmustine/mitomycin C), prior investigational treatment, radiotherapy and major surgery/open biopsy * 1 week since prior core biopsy * 1 month since prior thrombolytic agents * Concurrent full-dose anticoagulants with INR\>1.5 allowed if: In-range INR (usually between 2-3) on stable dose of oral anticoagulant or low molecular weight heparin, * OR; For patients on warfarin, the upper target for INR is ≤3 No active bleeding/pathological condition that carries a high risk of bleeding (e.g. tumor invading major vessels/known varices) * No evidence of CNS disease including primary brain tumor/brain metastasis * No other concurrent investigational agents - No concurrent major surgery * No concurrent combination antiretroviral therapy for HIV-positive patients * Clinically significant cardiovascular disease including: * Cerebrovascular accident within past 6 months, * Uncontrolled hypertension defined as BP\>150/100mmHg OR systolic BP\>180mmHg if diastolic BP\<90 mmHg, on ≥2 repeated determinations on separate days within past 3 months, * OR; Antihypertensive medications allowed as long as dose and number of antihypertensive medications have not increased within past 2 weeks, Myocardial infarction, coronary artery bypass graft, or unstable angina within past 6 months, OR; * OR; NYHA class III-IV congestive heart failure, serious cardiac arrhythmia requiring medication, or unstable angina pectoris within past 6 months, Clinically significant peripheral vascular disease within past 6 months * OR; pulmonary embolism, deep vein thrombosis, or other thromboembolic event within past 6 months