Entinostat, Nivolumab, and Ipilimumab in Treating Patients With Solid Tumors That Are Metastatic or Cannot Be Removed by Surgery or Locally Advanced or Metastatic HER2-Negative Breast Cancer

Inclusion Criteria: * Dose escalation: patients must have histologically or cytologically confirmed solid tumor malignancy that is metastatic or unresectable and for whom either standard curative or palliative measures do not exist or are no longer effective, or for whom anti-PD-L1/cytotoxic T-lymphocyte antigen (CTLA)-4 is appropriate * Dose expansion: patients must have histologically or cytologically confirmed invasive adenocarcinoma of the breast (human epidermal growth factor receptor 2 \[HER2\]-negative) that is locally advanced/metastatic and has progressed despite standard therapy; at least 1 prior chemotherapy regimen in the metastatic setting, and two lines of hormonal therapy (administered in the adjuvant or metastatic setting) for patients with hormone receptor-positive disease; NOTE: HER2-negativity will be defined per American Society of Clinical Oncology (ASCO)-College of American Pathologists (CAP) guidelines; patients whose tumors have HER2 immunohistochemistry (IHC) 3+, in situ hybridization (ISH) \>= 2.0, or average HER2 copy number \>= 6.0 signals per cell are not eligible * Age ≥ 18 years. * NOTE: Because no dosing or adverse event data are currently available on the use of these agents in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (Karnofsky \>= 70%) * Life expectancy of greater than 12 weeks * Hemoglobin (…