VEGF Trap and Docetaxel in Treating Patients With Persistent or Recurrent Ovarian Epithelial Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer

You may be eligible if

• Criteria:
• Histologically confirmed ovarian epithelial, primary peritoneal, or fallopian tube cancer:
• Persistent or recurrent disease
• Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques:
• * Must have \>= 1 target lesion to assess response;
• * Tumors within a previously irradiated field are considered nontarget lesions
• Must have received 1 prior platinum-based chemotherapy regimen (for primary disease) containing carboplatin, cisplatin, or other organoplatinum compound:
• Initial treatment may have included any of the following:
• High-dose therapy;
• Consolidation therapy;
• Extended therapy administered after surgical or nonsurgical assessment
• * AND Must have received 1 prior platinum-based chemotherapy regimen (for primary disease) containing carboplatin, cisplatin, or other organoplatinum compound:
• One additional cytotoxic regimen for recurrent or persistent disease allowed
• No history or evidence of CNS disease, including primary brain tumor or brain metastases
• Zubrod performance status 0-2 (0-1 for patients who received 2 prior regimens \[taxane and/or platinum regimens are counted separately\])
• Absolute neutrophil count \>= 1,500/mm\^3
• Platelet count \>= 100,000/mm\^3
• Hemoglobin \>= 9 g/dL
• Bilirubin normal
• aspartate aminotransferase / alanine aminotransferase (AST/ALT) \< 2.5 times upper limit of normal (ULN)
• Creatinine \< 1.5 times ULN OR creatinine clearance \> 60 mL/min
• Prothrombin Time (PT)/international normalized ratio (INR) \< 1.5 OR in-range INR 2-3 (if patient is on a stable dose of therapeutic warfarin or low molecular weight heparin)
• PTT \< 1.2 times control
• Urine protein:creatinine ratio \< 1
• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception during and for at least 6 months after completion of study treatment
• No active infection requiring antibiotics
• No sensory and motor neuropathy \>= grade 2
• No history of allergic reactions attributed to compounds of similar chemical or biologic composition to VEGF Trap, Magnevist, or fludeoxyglucose F 18
• No history of allergic reaction to paclitaxel or docetaxel or to products mixed in Cremophor EL or Tween 80
• No active bleeding or pathologic condition that would carry a high risk of bleeding, including any of the following:
• Known bleeding disorder; Coagulopathy; Peptic ulcer disease; Diverticulitis; Tumor involving major vessels
• No active and/or untreated pulmonary embolism, deep vein thrombosis, or other thromboembolic event (i.e., any condition associated with aberrant clotting or migration of an induced clot)
• No history or evidence of other CNS disease, including any of the following:
• Seizures not controlled with standard medical therapy; Cerebrovascular accident; Transient ischemic attack; Subarachnoid hemorrhage within the past 6 months
• No clinically significant cardiovascular disease, including any of the following:
• Uncontrolled hypertension (i.e., systolic blood pressure \[BP\] \> 150 mm Hg or diastolic BP \> 100 mm Hg; systolic BP \> 180 mm Hg and diastolic BP \< 90 mm Hg OR diastolic BP \> 90 mm Hg on \>= 2 measurements within the past 3 months); Myocardial infarction; Coronary or peripheral artery bypass graft
• No clinically significant cardiovascular disease, including any of the following:
• New York Heart association class III or IV congestive heart failure; Serious cardiac arrhythmia requiring medication; Peripheral vascular disease \>= grade 2; Unstable angina within the past 6 months; Clinically significant peripheral artery disease (e.g., claudication) within the past 6 months
• No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies
• Able to undergo an MRI scan:
• No claustrophobia; No implanted devices or metallic foreign bodies not compatible with MRI (e.g., ferromagnetic implants or pacemakers); No known history of allergic reaction to gadolinium contrast agents
• No other invasive malignancy within the past 5 years except nonmelanoma skin cancer
• No significant traumatic injury within the past 28 days
• Recovered from prior therapy to NCI Common Terminology Criteria for Adverse Events (CTCAE) version 3.0 grade =\< 1:
• Alopecia allowed
• No prior VEGF Trap
• No prior cancer treatment that would preclude study treatment
• Prior paclitaxel allowed
• Prior docetaxel for primary or recurrent disease allowed provided the following criteria are met:
• No disease progression during therapy; No disease relapse within 3 months of completing therapy; No persistent disease at the completion of primary therapy
• More than 7 days since prior placement of a vascular access device or core biopsy
• At least 1 week since prior hormonal therapy for the malignant tumor
• At least 4 weeks since other prior therapy, including immunologic agents (6 weeks for nitrosoureas or mitomycin C)
• More than 28 days since prior major surgery, open biopsy, dental extraction, or other dental surgery/procedure resulting in an open wound
• No concurrent major surgery
• No concurrent combination antiretroviral therapy for HIV-positive patients
• No other concurrent anticancer therapy
• No other concurrent investigational agents
• No concurrent hematopoietic growth factors during course 1 of phase I
• Concurrent hormone replacement therapy allowed
• White blood count (WBC) \>= 3,000/mm\^3