Between 8 and 18 adult female subjects will be enrolled and receive weekly paclitaxel in combination with increasing doses of fostamatinib. There will be three dosing intervals of fostamatinib (100 mg bid, 150 mg bid, and 200mg bid) selected based on prior phase I studies of single agent fostamatinib. Dose-escalation will follow a modified toxicity probability interval (mTPI) design. In this study, up to 18 adult female subjects will be enrolled and receive weekly paclitaxel in combination with fostamatinib at the MTD of the combination; at least 6 patients with receive fostamatinib plus paclitaxel at the MTD.