Sorafenib With or Without Paclitaxel and Carboplatin in Treating Patients With Recurrent Ovarian Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer

Inclusion Criteria: Diagnosis of ovarian epithelial, primary peritoneal, or fallopian tube cancer Recurrent disease Must have received a prior platinum-based regimen Platinum-sensitive (treatment-free interval > 6 months) No more than 2 prior chemotherapy regimens Measurable disease At least 1 unidimensionally measurable lesion >= 20 mm by conventional techniques OR >= 10 mm by spiral CT scan Not in a prior irradiation field No known brain metastases Performance status: ECOG 0-2 OR Karnofsky 80-100% Life expectancy: More than 12 weeks Hematopoietic: Absolute neutrophil count >= 1,500/mm3 Platelet count >= 100,000/mm3 Hemoglobin >= 9 g/dL No bleeding diathesis Hepatic: Bilirubin < 1.5 times upper limit of normal (ULN) AST or ALT =< 2 times ULN No history of allergic reaction attributed to compounds of similar chemical or biological composition to sorafenib or other agents used in the study Patients who have had a reaction to a taxane or a platinum and have not yet been rechallenged may undergo a desensitization regimen on study No hypersensitivity to paclitaxel or drugs using the vehicle Cremophor El: Prior hypersensitivity reaction to paclitaxel allowed provided rechallenged successfully Renal: Creatinine < 2 mg/dL Cardiovascular: Abnormal cardiac conduction (e.g., bundle branch block or heart block) allowed if stable for the past 6 months No symptomatic congestive heart failure No uncontrolled hypertension No cardiac arrhythmia No unstable angina pectoris; No myocardial infarction within the past 6 months Negative pregnancy test Fertile patients must use effective contraception Adequate intestinal function No concurrent requirements for IV hydration or nutritional support No active or ongoing infection No psychiatric illness or social situation that would preclude study compliance No other concurrent uncontrolled illness No other invasive malignancy with the past 5 years except nonmelanoma skin cancer More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) and recovered More than 3 weeks since prior hormonal therapy More than 4 weeks since prior radiotherapy and recovered No prior sorafenib No prior anticancer therapy that contraindicates study therapy No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin, or Hypericum perforatum (St. John's wort) No concurrent combination antiretroviral therapy for HIV-positive patients No concurrent therapeutic anticoagulation therapy Concurrent prophylactic low-dose warfarin allowed for maintenance of venous or arterial access devices No other concurrent anticancer therapies No other concurrent investigational agents Not pregnant or nursing