This study has two phases. The objective of Phase I to find the maximum dose (MTD) of Ruxolitinib when combined with standard dose of paclitaxel given weekly for advanced or metastatic breast cancer. Three participants will be entered at a dose ruxolitinib equaling 10 mg orally twice daily with weekly paclitaxel. If no dose-limiting toxicity is seen after 6 weeks of treatment (two cycles), then the dose of ruxolitinib will be escalated using a standard 3+3 design, until 2 participants experience dose limiting toxicity (DLT). The dose below the DLT is designated the MTD and this dose of ruxolitinib will be used in the phase II preoperative study for triple negative IBC.