In this study, patients with metastatic HER2-negative breast cancer will receive treatment with ixabepilone and sorafenib until disease progression or unacceptable toxicity occurs. The Phase I portion of this study will determine the maximum tolerated doses (MTDs) of sorafenib and ixabepilone that may be used in combination for first- or second-line treatment of MBC. The MTDs identified in the Phase I portion of the study will be used in the Phase II portion which will evaluate the efficacy and safety of the combination of sorafenib and ixabepilone in patients who have received at least one prior chemotherapy treatment in either the adjuvant or neoadjuvant setting or following one prior MBC chemotherapy in MBC patients who had not received prior adjuvant or neoadjuvant breast cancer chemotherapy. This will be one of the initial trials investigating the use of this treatment combination for MBC.