Patients receive paclitaxel IV over 3 hours on day 1, intraperitoneal (IP) cisplatin over 30-60 minutes on day 2, IP paclitaxel over 30-60 minutes on day 8, and doxorubicin HCl liposome IV over 1 hour on day 8. Patients not able to tolerate IP infusion receive paclitaxel IV and cisplatin IV on day 1 only. Treatment repeats every 28 days for 6 courses in the absence of disease progression or unacceptable toxicity.