The purpose of this study is to learn about the safety and side effects of combining entinostat, an investigational drug, with capecitabine, a drug commonly used in breast cancer (BC), in both participants with metastatic breast cancer (MBC) and then participants with high-risk breast cancer after neo-adjuvant therapy.

In order to identify the maximum dose that should be used in future participants, the first participants will start at a low dose of both drugs. If the participants on this dose level tolerate the treatment well without too many side effects, the next participants will receive a higher dose of one of the medications, and if those participants also tolerate the treatment well, then the drugs will continue to be increased with the next participants until a maximum dose that participants tolerate well is reached.

Participants in both groups will receive entinostat on days 1, 8, and 15 of each 21-day cycle and capecitabine on days 1-14 of each cycle. MBC participants may receive this treatment as long as they do not have disease progression or side effects that require them to stop study treatment while participants with high-risk BC after neo-adjuvant therapy will receive up to 8 cycles of study treatment as long as they do not have disease progression or side effects that require them to stop study treatment.

While participants are on study treatment, they will have regular physical exams and labs. After participants finish study treatment, they should be followed by their primary oncologist at least once a year. Study staff will also be in contact by phone at least once a year for 10 years.

Inclusion Criteria:

Disease Characteristics by Dose Escalation Phase and Expansion Phase:

Part A: Dose Escalation Phase:

1. Patients must have a histologically confirmed diagnosis of stage IV invasive breast cancer.
2. Patients can have breast cancer with positive OR negative estrogen and progesterone receptor status. Patients must have negative HER-2 receptor status. Estrogen, progesterone, and HER2 receptor status must be assessed according to ASCO/CAP guidelines. ER or PR positivity is defined as ≥ 1% positive nuclear staining. HER-2 is negative if tumor testing shows: a) IHC negative (0 or 1+) or b) ISH negative using single probe or dual probe. If HER-2 IHC is 2+, ISH must be performed and negative. HER-2 equivocal is not eligible.

Part B: Expansion Phase:

1. Patients must have a histologically confirmed diagnosis of stage I-III invasive breast cancer.

2. Patients with multifocal, multicentric, synchronous bilateral and primary inflammatory breast cancers are allowed.

   1. Multifocal disease is defined as more than one invasive cancer < 2 cm from the largest lesion within the same breast quadrant.
   2. Multicentric disease is defined as more than one invasive cancer ≥ 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants.
   3. Synchronous bilateral disease is defined as invasive breast cancer with positive lymph nodes (axillary or intramammary) in at least one breast, diagnosed within 30 days of each other. NOTE: The tumor with the highest recurrence score should be used.

3. Patients can have breast cancer with positive OR negative estrogen and progesterone receptor status. Patients must have negative HER-2 receptor status. Estrogen, progesterone, and HER2 receptor status must be assessed according to ASCO/CAP guidelines. ER or PR positivity is defined as ≥ 1% positive nuclear staining. HER-2 is negative if tumor testing shows: a) IHC negative (0 or 1+) or b) ISH negative using single probe or dual probe. If HER-2 IHC is 2+, ISH must be performed and negative. HER-2 equivocal is not eligible.

4. Patients must have been treated with standard neoadjuvant chemotherapy with at least three cycles of taxane or anthracycline based regimen. Patients must be registered within 36 weeks after last dose of chemotherapy.

5. Patients must have histologically confirmed residual invasive carcinoma at the time of surgery (ypT1mi or greater) or positive lymph nodes (ypN0(itc) or greater).

Both Phases:

1. Willingness and ability to provide written informed consent and to comply with the study protocol as judged by the investigator.

2. ECOG Performance Status of 0-2.

3. Age ≥ 18 years.

4. Subject must have a life expectancy ≥ 6 months.

5. Adequate bone marrow function defined as follows:

   1. Absolute neutrophil count (ANC) ≥ 1,000 cells/mm3
   2. Platelets ≥ 100,000 cells/mm3

6. Hemoglobin ≥ 9 g/dl (Note: The use of transfusion to achieve Hgb ≥ 9 g/dl is acceptable)Serum creatinine ≤ 1.5 x institutional upper limit normal (IULN) OR GFR ≥60 mL/min for patient with creatinine levels >1.5× institutional ULN

7. Bilirubin ≤ 1.5 x IULN OR Direct Bilirubin ≤ULN for patients with total bilirubin levels >1.5×ULN

8. ALT and AST ≤ 2.5 IULN

9. Alkaline Phosphatase ≤ 2.5 IULN

10. If a female is of childbearing potential, she has a negative serum blood pregnancy test during screening and a negative urine pregnancy test within 3 days prior to receiving the first dose of study drug. If the screening serum test is done within 3 days prior to receiving the first dose of study drug, a urine test is not required.

11. If a patient is of childbearing potential the patient must agree to use effective contraception during the study and for 120 days after the last dose of study drug.

    Non-childbearing potential is defined as (by other than medical reasons):

    1. ≥45 years of age and has not had menses for >2 years
    2. Amenorrheic for <2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pre-study (screening) evaluation
    3. Post hysterectomy, oophorectomy or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure otherwise the patient must be willing to use 2 adequate barrier methods throughout the study, starting with the screening visit through 120 days after the last dose of study drug

12. Non-vasectomized males must agree to use adequate contraception for at least 120 days after the last dose of study drug Males must also abstain from sperm donations for at least 120 days after the last dose of study drug.

13. Experienced resolution of toxic effect(s) of the most recent prior anti-cancer therapy to Grade ≤ 2 (except alopecia and Grade 3 neuropathy).

Exclusion Criteria (both phases):

1. Subjects who have had chemotherapy, biological therapy, immunological therapy, radiation therapy, or hormonal therapy within 3 weeks prior to first dose of study treatment.

2. Subjects who are unable or unwilling to discontinue use of prohibited medications.

3. Subject is unable or unwilling to participate in a study related procedure.

4. Subject is a prisoner.

5. Subject has evidence or history of an uncontrolled bleeding disorder. Patients with chronic bleeding disorders that are controlled with treatment or not clinically relevant are allowed.

6. Subjects with history of CNS disease including primary brain tumor, seizures not controlled with standard medical therapy, or history of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA), or subarachnoid hemorrhage within six months of first dose of study treatment.

7. Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks before first dose of study treatment AND enrolling in the metastatic dose escalation phase of present study only.

8. History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, or is not in the best interest of the patient to participate, in the opinion of the treating Investigator, including, but not limited to:

   1. Myocardial infarction or arterial thromboembolic events within 6 months prior to first dose of study treatment or severe or unstable angina, New York Heart Association (NYHA) Class III or IV disease, or a QTc interval > 470 msec.
   2. Uncontrolled hypertension (defined as BP >160/100) or diabetes mellitus.
   3. Another known malignancy that is progressing or requires active treatment.
   4. Any prior history of other cancer within the 2 years prior to first dose of study treatment with the exception of adequately treated non-melanoma skin cancer or cervical intraepithelial neoplasia [CIN]/cervical carcinoma in situ or melanoma in situ).
   5. Active infection requiring systemic therapy.

9. Any contraindication to oral agents or significant nausea and vomiting, malabsorption, or significant small bowel resection that, in the opinion of the investigator, would preclude adequate absorption.

10. Allergy to benzamide or inactive components of entinostat.

11. Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study.

12. Currently participating and receiving investigational therapy on another study. If prior participation in a study of an investigational agent/device, last dose of investigational therapy or use of an investigational device must be greater than 4 weeks from the first dose of study drug in the present study.

13. Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies), due to concerns for potential drug-drug interactions with entinostat and anti-retroviral medications.

14. Known active hepatitis B (e.g., hepatitis B surface antigen-reactive) or hepatitis C (e.g., hepatitis C virus ribonucleic acid [qualitative]). Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as the presence of hepatitis B core antibody [HBc Ab] and absence of HBsAg) are eligible. HBV DNA test must be performed in these patients prior to study treatment. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA.

15. If female, is pregnant or breastfeeding.

16. The following medications are prohibited while the patient is receiving entinostat:

    1. Any other HDAC Inhibitor, including valproic acid
    2. DNA methyltransferase inhibitors
    3. Any additional anticancer agents (excluding entinostat and capecitabine), such as chemotherapy, immunotherapy, targeted therapy, biological response modifiers, or endocrine therapy, will not be allowed, even if utilized as treatment of non-cancer indications.
    4. Any investigational agents.
    5. Radiation Therapy
    6. Traditional herbal medicines; these therapies are not fully studied and their use may result in unanticipated drug-drug interactions that may cause or confound the assessment of toxicity.