The purpose of this study is to decide the best dose of the study drug, PU-H71, that can be given in combination with the standard chemotherapy drug, nab-paclitaxel (Abraxane).

Inclusion Criteria:

• Age 18 years or older
• Signed informed consent
• Patients must have histologically confirmed HER2-negative breast cancer (defined as IHC 0 or 1+ and/or fluorescence in situ hybridization [FISH] < 2.0), that is metastatic in stage
• For estrogen receptor (ER)-positive breast cancer, patients must be considered refractory to endocrine therapy, having received and progressed through at least one prior line of endocrine therapy, or are intolerant of endocrine therapy
• All patients must have progressed on at least one line of cytotoxic therapy for metastatic disease
• Patients must have evidence of progressive disease
• Measurable or non-measurable disease as defined by Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1).
• Hematologic parameters: white blood cell (WBC) count of ≥ 3000/ul, absolute neutrophil count (ANC) ≥ 1500/ul, platelets ≥ 100,000/ul, hemoglobin ≥ 9.0 g/dl
• Non-hematologic parameters: bilirubin ≤ 1.5 mg/dl, AST/ALT ≤ 3.0 x upper limit of normal (ULN) (≤ 5.0 x ULN if liver metastases are involved)
• Serum creatinine < 1.5 xULN or CrCl > 40 mL/min (measured or calculated using the Cockcroft-Gault formula)
• An Eastern Cooperative Oncology Group performance status of 0-2
• Life expectancy of 3 months or more as assessed by the investigator
• Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures
• Negative β-human chorionic gonadotropin (hCG) pregnancy test for premenopausal women of reproductive capacity (those who are biologically capable of having children) and for women less than 12 months after menopause.
• Women of childbearing potential must agree and commit to the use of a highly effective method of contraception. Men must agree and commit to use a barrier method of contraception while on treatment and for 3 months after last dose of investigational products.

Exclusion Criteria:

• Symptomatic brain or CNS metastases. Previously treated and stable CNS disease is allowed.
• Any of the following for the treatment of cancer within 2 weeks of first study treatment: chemotherapy, immunotherapy, experimental therapy, or biologic therapy.
• Radiation therapy (other than palliative radiation to bony metastases) as cancer therapy within 4 weeks prior to initiation of study treatment
• Any major surgical procedure within 4 weeks of first study treatment
• Prior treatment with Abraxane
• Active liver disease, including viral or other hepatitis, or cirrhosis
• Pregnancy or lactation
• Other active infections aside from hepatitis
• Any other significant medical condition not under control, including any acute coronary syndrome within the past 6 months.
• Patients with a permanent pacemaker
• Patients with a QTc > 480 ms in the baseline EKG
• Surgery, radiotherapy, or lesion ablative procedure to the only area of measurable/evaluable disease
• Peripheral neuropathy of grade ≥ 2 per NCI CTCAE, Version 4.0, at the time of or within 3 weeks prior to the first study therapy
• Other medications, or severe acute/chronic medical or psychiatric condition, or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results in the judgment of the investigator
• History of an invasive second primary malignancy diagnosed within the previous 3 years, except for appropriately treated stage I endometrial or cervical carcinoma or prostate carcinoma treated surgically, and non-melanoma skin cancer.