PVX-410 Vaccine Plus Pembrolizumab in HLA-A2+ Metastatic Triple Negative Breast Cancer

Inclusion Criteria: * Willing and able to provide written informed consent for the study. * Female aged ≥18 years on the day of signing informed consent. * HLA A2+ by deoxyribonucleic acid (DNA) sequence analysis (by history with documentation or as part of this study). * Histopathological diagnosis of metastatic or inoperable locally advanced TNBC that meets the following criteria: --Triple negative defined as Estrogen Receptor (ER)\<1%, Progesterone Receptor (PR)\<1%, and Human Epidermal Growth Factor Receptor 2 (HER2) negative according to American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines by local testing according to institutional standards. * For tumors with equivocal interpretation of receptor status (e.g., ER/PR ≥1% "weak" or "faint" staining), the Principal Investigator will have final determination of triple-negative status. For tumors with discrepant receptor results between 2 or more biopsies (including metastatic and/or early stage biopsies), the Principal Investigator will have final determination of triple negative status, but in general the most recent biopsy can be used for eligibility purposes. If receptor testing is not available on a metastatic biopsy, the primary tumor test result is acceptable. * Metastatic or inoperable locally advanced disease is defined as either: histologically confirmed metastatic breast cancer by biopsy; or locally advanced breast cancer that, in the opinion of the treating physician, is not amenable to curative intent surgical resection; or, radiological or clinical evidence suggestive and supportive of metastatic disease without a documented metastatic biopsy, provided the patient has a prior diagnosis of TNBC that otherwise meets the eligibility criteria. --Ductal, lobular, mixed, or metaplastic histology. * Measurable disease, as determined by RECIST 1.1. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (see Appendix section 16.1) * At least one line of prior systemic therapy for metastatic or recurrent breast cancer (there is no limit to the number of prior therapies). * Adequate normal organ and marrow function within 10 days of planned treatment initiation, as defined below: Hematologic * Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/L without transfusion or erythropoietin dependency (within 7 days of assessment) * Absolute neutrophil count (ANC) ≥1.5x10\^9/L (≥1500 per mm3) * Platelet count ≥100x109/L (≥100,000 per mm3) Renal * Serum creatinine ≤1.5 x the upper limit of normal (ULN) OR measured or calculated creatinine clearance ≥60 mL/min for patients with creatinine levels \>1.5 x institutional Upper Limit of Normal (ULN) (calculated per institutional standard). (Glomerular filtration rate can be used in place of creatinine or creatinine clearance.) Hepatic * Serum bilirubin ≤1.5 x institutional ULN OR direct bilirubin ≤ ULN for patients with total bilirubin levels \>1.5 x ULN * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) ≤2.5 x institutional ULN OR ≤5 x ULN for patients with known liver metastases. * Albumin ≥2.5 mg/dL Coagulation * International normalized ratio (INR) or prothrombin time (PT) ≤1.5 x ULN, unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Activated partial thromboplastin time (aPTT) ≤1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants Other * Lactate Dehydrogenase (LDH) ≤1.5 x institutional ULN * Willing to provide archived tissue for correlative studies. If no archived sample is available the patient will still be eligible. * Negative virology/serology for human immunodeficiency virus (HIV)-1, HIV-2, hepatitis B surface antigen (HBsAg), and hepatitis C virus (HCV) DNA. * Either of non-reproductive potential (i.e., post-menopausal by history of age ≥50 years old and no menses for ≥1 year without an alternative medical cause; OR history of hysterectomy, history of bilateral tubal ligation, or history of bilateral oophorectomy) OR must have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study treatment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * If of childbearing potential (i.e., does not meet criteria for non-reproductive potential above), willing to use 2 methods of birth control, or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study treatment * Willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations, including follow-up Exclusion Criteria: * Currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of study treatment. * Previous enrollment in the present study. * Mucinous or tubal histology or other good prognosis histology. * Known hypersensitivity to any component of PVX-410, Hiltonol®, Montanide, pembrolizumab, or excipients. * Receipt of the last dose or treatment of anti-cancer chemotherapy, radiotherapy, surgery, endocrine therapy, targeted therapy, biologic therapy, or tumor embolization ≤2 weeks (4 weeks for any monoclonal Antibody (mAb), 6 weeks for nitrosoureas or mitomycin C) prior to first dose of study treatment, or has not recovered (i.e., to ≤Grade 1 or Baseline) from clinically significant Adverse Events (AEs) due to these previously administered agents. * Patients with ≤Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Subjects with other irreversible toxicity (e.g., hearing loss) or reversible toxicity (e.g. alopecia) that is not reasonably expected to be exacerbated by the investigational product and is not expected to interfere with study participation may be included. * If patient received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Received a live vaccine within 30 days of planned start of study therapy. --Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed. * Ongoing or planned systemic anti-cancer therapy or radiation therapy. * Pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the pre-screening or screening visit through 120 days after the last dose of study treatment. * Has a known history of active Tuberculosis (Bacillus Tuberculosis). * History of allogeneic organ transplant. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least 4 weeks prior to the first dose of study treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for management of brain metastases for at least 7 days prior to study treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. * Known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. * Diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid. * Active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment. * Known history of non-infectious pneumonitis that required steroids or any evidence of active pneumonitis. * Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * History or current evidence of any other 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