I. To collect safety and toxicity data as well as the feasibility and response rate where hormonal therapy is added to the combination under investigation at the time of progressive disease. (Exploratory) II. To determine the pharmacokinetic profile of 5-AZA (full profile) and entinostat (trough concentrations) in patients with advanced breast cancer. (Exploratory) III. To assess serum cytidine deaminase pharmacogenetics and phenotypic activity as a potential biomarker of response to 5-AZA. (Exploratory) IV. To evaluate baseline and change in candidate gene re-expression (e.g., estrogen receptor [ER] alpha, retinoic acid receptor [RAR] beta) in malignant tissue obtained from selected patients through fine-needle aspiration (FNA) and core biopsy, prior to and following combination therapy. (Exploratory) V. To evaluate baseline and change in gene methylation silencing in circulating deoxyribonucleic acid (DNA) obtained prior to and following combination therapy. (Exploratory) VI. To evaluate baseline and change in gene methylation in malignant tissue obtained through FNA and core biopsy. (Exploratory)