BN-Brachyury, Entinostat, Adotrastuzumab Emtansine and M7824 in Advanced Stage Breast Cancer (BrEAsT)

Background: * Current greater than or equal to 2nd line treatments for metastatic breast cancer provide modest response rates, and modest improvement in progression-free survival but no treatments are curative. * Bavarian-Nordic (BN)-Brachyury vaccine is a recombinant poxvirus vaccine against the transcription factor brachyury, which plays an important role in the epithelial-to-mesenchymal transition in breast cancer. A recently completed phase 1 study of BN-Brachyury vaccine showed the vaccine was well tolerated and generated an immune response. * M7824 (Bintrafusp alfa) is a novel bifunctional fusion protein composed of a monoclonal antibody against human programmed death-ligand 1 (PD-L1) fused to the soluble extracellular domain of human transforming growth factor (TGF)-Beta receptor II (TGF-BetaRII(241-R2), which functions as a TGF-Beta trap. * Ado-trastuzumab emtansine (T-DM1 or Kadcyla) is an antibody drug conjugate used in second- and third- line treatment of metastatic human epidermal growth factor receptor 2 (HER2+) breast cancer (HER2+BC). T-DM1 activates antibody-dependent cellular cytotoxicity (ADCC), dendritic cell maturation, increases tumor infiltrating lymphocytes (TILs), increased PD-L1 expression, and increased immunomodulatory cytokines. * Entinostat is a class 1 histone deacetylase inhibitor (HDACi) which suppresses tumor initiating cells, regulatory T-cells and myeloid-derived suppressor cells (MDSCs), as well as enhances cytotoxic T-cell mediated lysis, direct natural killer (NK) lysis, NK cell activation, increases PD-L1 expression and antibody-dependent cellular cytotoxicity (ADCC). In addition, entinostat may also be able to overcome HER2 resistance. * We propose a Phase 1b trial to evaluate the safety and efficacy of the stepwise combination of the BN-Brachyury vaccine, M7824, T-DM1 and entinostat in metastatic breast cancer. * Arm 1 - Triple Negative Breast Cancer (TNBC); M7824 + BN-Brachyury * Arm 2 - estrogen receptors (ER)-/progesterone receptors (PR-)/HER2+ Breast Cancer; M7824 + BN-Brachyury + T-DM1 * Arm 3 - ER-/PR-/HER2+ Breast Cancer; M7824 + BN-Brachyury + T-DM1+ Entinostat Objectives: Primary Objectives: * Arms 1-3: Overall response rate (overall response rate (ORR); partial response (PR)+complete response (CR) * Arms 1-3: Safety for each of the three combinations of agents explored in the arms Eligibility: Selected Inclusion Criteria * Histologically confirmed metastatic breast cancer with appropriate immunohistochemistry (IHC) testing by a certified lab: * For Arm 1: Triple negative breast cancer. Hormone receptor negative is defined by estrogen receptor \< 10% and progesterone receptor \< 10%. HER2 negative breast cancer is defined as HER2 per IHC 0 or 1+ or 2+ with negative fluorescence in situ hybridization (FISH). * For Arms 2 and 3: Hormone receptor negative, HER2+ breast cancer as defined by estrogen receptor \< 10% and progesterone receptor \< 10%. HER2 positive as per IHC 3+ or 2+ with positive FISH. * Prior treatment: * For Arm 1: greater than or equal to 1 prior therapy in the metastatic setting. Patients with known PD-L1 positive tumors must have received prior treatment with atezolizumab + nab-paclitaxel. Patients with ER 1-9% must have received treatment with at least two lines of endocrine treatment (selective estrogen receptor modulators (SERM), AI, fulvestrant) with one prior treatment including a cyclin-dependent kinase 4 (CDK4)/6 inhibitor + endocrine therapy for their metastatic cancer and should be considered endocrine therapy resistant. * For Arms 2 and 3: greater than or equal to 1 prior treatment in the metastatic setting with a taxane (docetaxel or paclitaxel), herceptin and pertuzumab. * Females or males greater than or equal to 18 years old * Eastern Cooperative Oncology Group (ECOG) 0 or 1 * Measurable metastatic disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * For Cohort 3, Arms 2 and 3: At least one biopsiable lesion and willingness to undergo up to three research biopsies. * Adequate hematopoietic, hepatic, renal and cardiac (ejection fraction (EF) greater than or equal to 50%) function. Selected Exclusion Criteria * Patients who have received chemotherapy, including trastuzumab and pertuzumab in the previous 3 weeks; other investigational agents within 4 weeks or a programmed cell death protein 1 (PD-1)/PD-L1 antibody within 4 weeks prior to study enrollment; radiotherapy less than or equal to 4 weeks of study entry. * Symptomatic central nervous system (CNS) metastases and leptomeningeal disease are excluded but treated brain metastases (no radiotherapy within 6 weeks) or asymptomatic brain metastasis are allowed. * History of invasive malignancy less than or equal to 3 years prior to enrollment. * History of congestive heart failure (CHF) as defined as New York Heart Association (NYHA) class 3 or 4 or hospitalization for CHF (any NYHA class) within 6 months of trial start. * Concurrent use of chronic systemic steroids except for physiologic systemic steroids for replacement defined as 10mg of prednisone or an equivalent dose. Design: This study contains three separate, single arm phase 1b trials. * Arm 1 will evaluate M7824 and BN-Brachyury in patients with triple-negative breast cancer (TNBC). * If this doublet is determined to have acceptable toxicity (0-1 dose limiting toxicities (DLTs) of the first 6 patients), up to 19 patients will be enrolled on Arm 2 in which BN-Brachyury, M7824 and T-DM1 will be evaluated in patients with advanced HR-/HER2+ BC with disease progression after treatment with docetaxel (THP) or intolerance to THP. * If this triplet is determined to have acceptable toxicity (0-1 DLTs of the first 6 patients), 19 patients will be enrolled on Arm 3 in which BN-Brachyury, entinostat, M7824 and T-DM1 will be evaluated in patients with advanced HR-/HER2+ BC with disease progression after treatment with THP or intolerance to THP. * Up to 51 evaluable patients will be recruited for this study, with an accrual ceiling set at 65 patients. Trial Drugs * BN-Brachyury vaccine every 3 weeks until cycle 9, then every 12 weeks: * Recombinant MVA-BN-Brachyury (R2PD): 4 injections of vaccines with 1 given subcutaneous (SC) in each extremity on Day 1 of Cycles 1 and 2. Each injection of MVA-BN-Brachyury consists of 2.0 x 10(8) infectious units (Inf.U). * Recombinant fowlpox virus (FPV)-Brachyury: 1 injection given SC in one extremity on Day 1 of Cycles 3 and beyond. Each infection of FPV-Brachyury consists of 1.0 x 10(9) Inf.U. * adotrastuzumab emtansine (T-DM1) 3.6mg/kg via intravenous (IV) infusion every (q)3 weeks on Day 1 of each cycle. * M7824 2,400mg via IV infusion q3 weeks on Day 1 of each cycle. * Entinostat 5mg by mouth weekly recommended phase 2 dose (RP2D) administered by patient on Days 1, 8 and 15 of each cycle.