Two Different Schedules of Carboplatin, Paclitaxel, Gemcitabine, and Surgery in Treating Patients With Newly Diagnosed Stage IIIC or Stage IV Primary Epithelial Ovarian Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cancer

OBJECTIVES: * To examine and compare the feasibility of two sequential neoadjuvant regimens in patients with newly diagnosed, stage IIIC-IV ovarian or peritoneal carcinoma. * To confirm the feasibility of extended sequential regimens offering 6+6 courses of chemotherapy in patients presenting with inoperable disease. * To establish the feasibility of biweekly paclitaxel with vs without gemcitabine hydrochloride in the adjuvant phase, after carboplatin neoadjuvant induction. OUTLINE: This is a multicenter study. Patients are stratified according to serum albumin (\< 30 g/dL vs 30-35 g/dL vs \> 35 g/dL), FIGO stage (stage IIIC vs stage IV), and histological grade (well-differentiated \[grade 1\] vs moderately well-differentiated \[grade 2\] vs poorly differentiated \[grade 3\]). Patients are randomized to 1 of 2 treatment arms. * Neoadjuvant therapy: * Arm I: Patients receive carboplatin IV over 1 hour and gemcitabine hydrochloride IV over 30 minutes on days 1 and 8. Treatment repeats every 3 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity. * Arm II: Patients receive carboplatin IV over 1 hour on day 1. Treatment repeats every 3 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity. In both arms, patients with disease progression are switched to adjuvant paclitaxel-based chemotherapy. Patients with responding disease after switching regimens may undergo debulking surgery at the investigator's discretion. * Surgery: After completion of 6 courses of chemotherapy, all patients are evaluated for surgery. Patients with questionable operability based on clinical or radiological criteria are re-assessed laparoscopically. Patients judged to have disease that is amenable to optimal debulking at laparotomy are recommended for debulking surgery. Patients judged to have disease that is not amenable to optimal debulking are reconsidered for surgery after they receive an additional 6 courses of chemotherapy. Patients with disease progression after completion of 12 courses of chemotherapy undergo laparotomy only if there is a clinically pressing need to palliate their condition and if surgery offers some prospect of achieving this result (e.g., palliation for bowel obstruction). * Adjuvant therapy: * Arm I: Patients receive paclitaxel IV over 3 hours on day 1. Treatment repeats every 2 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity. * Arm II: Patients receive paclitaxel IV over 3 hours and gemcitabine hydrochloride IV over 30 minutes on day 1. Treatment repeats every 2 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients complete quality of life questionnaires at baseline, after completion of course 6 of neoadjuvant therapy, before course 7, and at the end of study treatment. After completion of study therapy, patients are followed periodically for up to 10 years.