TAEK-VAC-HerBy Vaccine for Brachyury and HER2 Expressing Cancer

Inclusion Criteria: General inclusion criteria, apply to all cohorts: * Men and women ≥18 years old. * Patients must have histologically documented malignant tumor which is unresectable locally advanced or metastatic. * ECOG performance status 0 or 1 * Patients must have normal organ and bone marrow function as defined in the protocol. * Normal left ventricular ejection fraction (LVEF) ≥50%. * Troponin I within normal limits. * A maximum cumulative dose of prior doxorubicin ≤360 mg/m2 or epirubicin ≤720 mg/m2 * Any approved cancer therapy (except HER2 antibodies) must be completed at least 3 weeks or 5 half-lives for small molecule inhibitors, whichever is shorter, prior to the first planned dose of TVH vaccine. * HER-2 positive cancer: Patients are required to be on active treatment with HER2 antibodies (trastuzumab) prior to and during study treatment. * Chordoma patients with progressive extracranial chordoma (base of skull is permitted) not amenable for surgical resection with curative intent, nor for radiation therapy will be enrolled. * Patients must have recovered (Grade 1 or baseline) from any clinically significant toxicity associated with prior therapy. * Patients must have measurable disease by computed tomography (CT) or magnetic resonance imaging (MRI) per RECIST 1.1. Exclusion Criteria: * Known metastatic disease to the central nervous system, unless previously treated and responded with a minimum stable disease over 2 CT scans separated at least 4 weeks from each other, and more than 6 weeks since the last dose of dexamethasone. * History of allergy or untoward reaction to prior vaccination with vaccinia virus, aminoglycoside antibiotics, ciprofloxacin, or egg products. * Subjects should have no known evidence of being immunocompromised. * Chronic administration (defined as \>5 consecutive days of \>15 mg of prednisone (or equivalent) per day) of systemic corticosteroids within 14 days of the first planned dose of TAEK-VAC-HerBy vaccine. Use of inhaled steroids, nasal sprays, eye drops, and topical creams is allowed. Steroids premedication for CT scans is allowed. * Clinically significant cardiomyopathy, coronary disease, congestive heart failure (NYHA class III or IV) or reduced as per institutional standards LVEF, poorly controlled hypertension (systolic \>180 mm Hg or diastolic \>100 mm Hg) or cerebrovascular accident within 1 year. * Known history of, or any evidence of active, non-infectious pneumonitis or primary pulmonary fibrosis.