This phase I trial is studying the side effects and best dose of intraperitoneal infusions of carboplatin when given together with intravenous infusions of either docetaxel or paclitaxel followed by intraperitoneal paclitaxel in treating patients with stage II, stage III, or stage IV ovarian epithelial, fallopian tube, or primary peritoneal cavity carcinoma (cancer). Drugs used in chemotherapy, such as carboplatin, docetaxel, and paclitaxel, work in different ways to stop tumor cells from dividing so they stop growing or die. Combining more than one drug and giving them in different ways may kill more tumor cells