ACY-1215 + Nab-paclitaxel in Metastatic Breast Cancer

Inclusion Criteria: 1. Subjects have histologically confirmed adenocarcinoma of the breast -- all breast cancer subtypes are allowed. 2. Unresectable or metastatic breast cancer. Locally recurrent disease must not be amenable to any local treatment with curative intent. Metastatic disease must be demonstrated either radiographically or histologically. 3. Patients may have measurable disease only, non-measurable disease only, or both (RECIST 1.1). 4. ECOG performance status of 0-1. 5. Must have recovered from the acute toxic effects of all prior therapy prior to registration for this study to grade 1 or less. 6. Women and men of all races and ethnic groups are eligible for this trial. 7. Minimum number of prior treatments required given standard nab-paclitaxel dosing: * If HER2 negative: none * If HER2 positive: two prior regimens containing HER2 targeted therapies in the inoperable locally advanced and/or metastatic setting. Prior therapy for inoperable locally advanced/metastatic disease should include trastuzumab plus pertuzumab as well as ado-trastuzumab. Pertuzumab and ado-trastuzumab must have been previously used, unless for reasons that include, but are not limited, to the following: intolerance to pertuzumab and/or ado-trastuzumab, medical contraindication, regimen declined by patient, treating investigator discretion, or medical insurance coverage issues which prevented administration of pertuzumab or ado-trastuzumab. These reasons must be reviewed with the study chairs and documented in the medical record and care report form. Patients who relapse within 12 months of completing neoadjuvant/adjuvant pertuzumab or ado-trastuzumab would be considered as having progressed on that regimen. There is no maximum number of prior treatments allowed in the metastatic setting. 8. Age \>18 years. Because breast carcinoma is a disease of adults that rarely occurs in children, children are excluded from this study. 9. Patients must have normal organ and marrow function as defined below: * leukocytes ≥3,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * hemoglobin ≥9 g/dL * total bilirubin ≤ 1.5 × the upper limit of normal * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal * Serum creatinine ≤ 1.5 × the upper limit of normal or calculated creatinine clearance ≥ 60 mL/min 10. Subject is capable of understanding the informed consent process. 11. The effects of ACY-1215 on the developing human fetus are unknown. For this reason and because the effects of chemotherapy are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 2 weeks after completion of ACY-1215 administration. Exclusion Criteria: 1. Patients who have had chemotherapy, hormonal therapy, or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier. Concomitant treatment with bone-targeted therapies such as RANKL inhibitors or bisphosphonates is allowed. 2. Patients who are receiving any other investigational agents concurrently or have received investigational agents within 2 weeks or 5 half-lives of the compound or active metabolites, whichever is longer before the first dose of the study treatment. 3. Patients who have received HDAC inhibitors (including valproic acid, entinostat, vorinostat) are excluded 4. Subject is pregnant or nursing. Pregnant women are excluded from this study because ACY-1215 is an investigational therapy with unknown potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ACY-1215, breastfeeding should be discontinued if the mother is treated with ACY-1215. 5. Symptomatic or unstable brain metastases. (Note: Asymptomatic patients with metastatic brain disease who have been on a stable dose of corticosteroids for treatment of brain metastases for at least 14 days prior to registration are eligible to participate in the study). 6. HIV+ with a CD4 count \<200 are ineligible because these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. 7. Patients receiving any medications or substances that are strong inhibitors of CYP450 3A4 isoenzyme. 8. History of allergic reactions attributed to compounds of similar chemical or biologic composition to nab-paclitaxel. 9. Uncontrolled intercurrent illness including but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 10. Corrected QT interval (QTc) value \> 480 msec at screening; family or personal history of long QTc syndrome or ventricular arrhythmias including ventricular bigeminy at screening; previous history of drug-induced QTc prolongation or the need for treatment with medications known or suspected of producing prolonged QTc intervals on electrocardiogram (EKG). If QTc prolongation on screening ECG is felt to be related to electrolyte imbalance, an EKG can be repeated after correction of electrolytes.