PHASE I (COURSES 1-3): Patients receive ruxolitinib phosphate orally (PO) twice daily (BID) on days 1-21, paclitaxel intravenously (IV) over 1 hour on days 1, 8, and 15, and carboplatin IV over 30 minutes on day 1. Treatment repeats every 21 days for 3 courses in the absence of disease progression or unacceptable toxicity. Within 6 weeks after completion of course 3, patients undergo tumor reductive surgery (TRS).