PHASE I (COURSES 4-6): Within 4 weeks of TRS, patients receive ruxolitinib phosphate PO BID on days 1-21, paclitaxel 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. If TRS is not performed due to non-response or medical contraindications and criteria for discontinuation of protocol therapy have not been met, patients should resume ruxolitinib phosphate, paclitaxel, and carboplatin within 6 weeks of completing course 3 of therapy.