Combination Chemotherapy and Autologous Peripheral Stem Cell Transplant in Treating Patients With Stage III, Stage IV, or Recurrent Ovarian Epithelial Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer

OBJECTIVES: * To establish the maximum tolerated dose (MTD) of continuous infusion intravenous topotecan hydrochloride when administered with intraperitoneal (IP) cisplatin and intravenous melphalan in patients with stage III, stage IV, or recurrent ovarian epithelial cancer, primary peritoneal cancer, or fallopian tube cancer. * To describe the toxicities of each dose studied. * To evaluate the pharmacokinetics of topotecan hydrochloride when administered at the maximum tolerated dose and cisplatin. * To confirm the pharmacokinetic advantage of high-dose IP cisplatin and IP paclitaxel. * To obtain tissue at the time of peritoneal catheter placement in order to evaluate the molecular determinants of apoptosis (including p53 status, p21 gene expression, bcl-2 gene expression, and bcl-2/bax ratio) and the extent of apoptosis by the TdT assay. * To evaluate the molecular determinants of DNA damage and repair, including expression levels of ERCC1 and MDR1, and HER2/neu expression by immunohistochemistry. OUTLINE: This is a dose-escalation study of topotecan hydrochloride. Patients undergo surgical placement of an intraperitoneal (IP) catheter. Tumor biopsies are obtained during surgery for laboratory analysis of molecular determinants of apoptosis (including p53 status, p21 gene expression, bcl-2 gene expression, bcl-2/bax ratio) and molecular determinants of DNA damage and repair (including expression levels of ERCC1 and MDR1, and HER2/neu expression by immunohistochemistry). The extent of apoptosis is also assessed using the TdT assay. * Course 1: Patients receive paclitaxel IP on day 1, cyclophosphamide IV on day 2, and filgrastim (G-CSF) subcutaneously (SC) beginning on day 3 and continuing until apheresis is completed. Patients undergo apheresis until ≥ 2.5 X 10\^6 CD34-positive cells/kg are collected. Two weeks later, patients proceed to course 2. * Course 2: Patients receive cisplatin IP and melphalan IV on days -11 and -4 and topotecan hydrochloride by continuous infusion over 120 hours on days -10 to -6. Patients receive 25% of their peripheral blood stem cells (PBSCs) on day -3 and G-CSF IV beginning on day -3 and continuing until blood counts recover. Patients receive their remaining PBSCs on day 0. Patients undergo daily blood sample collection during topotecan hydrochloride administration for pharmacokinetic studies. Patients treated at the maximum tolerated dose of topotecan hydrochloride undergo additional blood sample collections for pharmacokinetic studies. After completion of study therapy, patients are followed every 3 months.