Phase II Study of Clinical Activity of Pegaspargase in Women With Relapsed or Refractory Epithelial Ovarian Cancer, Fallopian Tube Cancer, and/or Primary Peritoneal Cancer

Background: * The bacterial enzyme L-asparaginase (L-ASP) catalyzes hydrolysis of asparagine to aspartate and is used to treat acute lymphoblastic leukemia (ALL).Studies demonstrated in vitro cytotoxic activity against solid tumor types including ovarian cancer. * Our laboratory demonstrated L-ASP inhibits vascular remodeling and modulates heterotypic adhesion interactions between ovarian cancer cells and endothelial cells. Results indicate L-ASP has the ability to modify the local tumor microenvironment. * Epithelial ovarian cancer requires neovascularization for growth and metastasis. Anti-angiogenesis agents show promise in treatment of recurrent disease. * The pegylated form of L-ASP, pegaspargase, (Sigma Tau ONCASPAR (Trademark)) is shown to deplete serum levels of asparagine and is approved for ALL. ONCASPAR is in clinical trial with gemcitabine for pancreatic cancer and other solid tumors. * Recommended dose of pegaspargase in ALL is 2,500 IU/m\^2 every two weeks intramuscular (IM)/intravenous (IV). IM dosing of 2,000 IU/m\^2 every two weeks has been studied in a phase I protocol with various solid tumors. * Demonstration of safety and anti-angiogenic activity will lead to combination studies. Primary Objectives: * To preliminarily evaluate the anti-tumor activity of pegaspargase, 2,000 IU/ m\^2 every two weeks intravenous (IV) (or intramuscular (IM)) and explore associations with toxicity and clinical outcome. * To evaluate the safety of pegaspargase in patients with recurrent or refractory ovarian, fallopian tube, and/or primary peritoneal cancer. Secondary Objectives: * To explore changes in circulating angiogenic cytokines after treatment with pegaspargase. * To measure apoptosis and proliferation in tumor (or malignant effusion) by protein array before and during therapy. * To evaluate changes in tumor vascularity using dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI). Eligibility: * Women with epithelial ovarian cancer, fallopian tube cancer, and/or primary peritoneal cancer that is persistent, relapsed and/or refractory to prior therapy. * There is no limit to number of prior treatment regimens. Patients may not have previously received L-ASP. * Women must have disease amenable to biopsy or malignant effusions (pleural effusion or ascites) that may be serially tapped. * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, 2. * Evidence of adequate end organ function and normal coagulation parameters (prothrombin time (PT), activated partial thromboplastin time (aPTT)). Design: * Women will receive 2,000 IU/m\^2 of pegaspargase intravenously every two weeks in 28-day cycles until disease progression, excessive toxicity, or withdrawal from study. * Biopsy of tumor and dynamic contrast-enhanced-magnetic resonance imaging (MRI) will be performed prior to starting pegaspargase (mandatory) and after 6 weeks of treatment (optional). * Clinical outcome will be measured and correlated with biological endpoints. * Research blood samples will be taken to assess changes in serum vascular endothelial growth factor (VEGF), interleukin-6 (IL6), and interleukin-8 (IL8). * Blood will be collected to evaluate circulating endothelial cells. * Patients will be seen in clinic every 4 weeks and outcome measured every other cycle.