Safety and Tolerability Trial (MVA-BN-Brachyury/FPV-Brachyury)

Inclusion Criteria: * Patients must have a metastatic or unresectable locally advanced malignant solid tumor, histologically confirmed by the Laboratory of Pathology, NCI. In the case of chordoma, unresectable, locally recurrent, or metastatic tumors are acceptable for enrollment, given that this represents incurable disease. Efforts will be made, as much as possible, to enroll patients with tumor types with known increased expression of brachyury (such as lung, breast, ovarian, prostate, colorectal, pancreatic, hepatocellular, Merkel cell, small cell lung cancer or chordoma; other tumors may be included as data on the level of brachyury in those tumors becomes available). Every attempt will be made to collect archival tissue, preferably metastatic disease. * Patients may have measurable or nonmeasurable but evaluable disease. Patients with surgically resected metastatic disease at high risk of relapse or patients with metastatic disease with a complete response after palliative chemotherapy with at high risk of relapse (such as small cell lung cancer, etc) are also eligible. * Prior therapy: Patients must have completed or had disease progression on at least one prior line of disease-appropriate therapy for metastatic disease, or not be candidates for therapy of proven efficacy for their disease. * There should be a minimum of 4 weeks from any prior chemotherapy, immunotherapy and/or radiation, with the following exceptions: 1. Prostate cancer - patients must continue to receive GnRH agonist therapy (unless orchiectomy has been done). Patients on combined androgen blockade therapy may continue those therapies as well (bicalutamide, nilutamide, flutamide, enzalutamide and abiraterone). 2. Breast cancer - patients may remain on hormonal therapy if indicated (ER/PR+), HER2-directed therapy for HER2+ breast cancer (3+ IHC or FISH+). 3. EGFR-mutated lung cancer - patient may remain on first line EGFR inhibiting therapy (tyrosine kinase inhibitors) if they have had stable disease or ongoing response to therapy. Patients with T790M mutations may continue receiving osimertinib while receiving vaccine. 4. Mestastatic colorectal cancer may continue "maintenance" therapy with capecitabine and/or bevacizumab. * There should be a minimum of 6 weeks from any prior antibody therapies, (such as ipilimumab or anti-PD1/PDL1) due to prolonged half-life. * Patients must have recovered (grade 1 or baseline) from any clinically significant toxicity associated with prior therapy. * Age ≥ 18 years. * ECOG performance status ≤ 1 (Karnofsky ≥ 70%) * Patients must have normal organ and marrow function as defined in protocol * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to trial entry and for the duration of trial participation and for a period of 4 months after the last vaccination therapy.) * Patients must be able to understand and be willing to sign a written informed consent document. Exclusion Criteria: * Concurrent treatment for cancer, with specific exceptions noted in inclusion criteria. * Chronic hepatitis B or C infection. * Any significant disease that, in the opinion of the investigator, may impair the patient's tolerance of trial treatment. * Significant dementia, altered mental status, or any psychiatric condition that would prohibit the understanding or rendering of informed consent. * Active autoimmune diseases requiring treatment or a history of autoimmune disease that might be stimulated by vaccine treatment. * Concurrent use of systemic steroids, except for physiologic doses of systemic steroid replacement or local (topical, nasal, or inhaled) steroid use. Limited pharmacologic doses of systemic steroids (e.g., in patients with exacerbations of reactive airway disease or to prevent I.V. contrast allergic reaction or anaphylaxis in patients who have known contrast allergies) are allowed. * Patients who are receiving any other investigational agents within 28 days before start of trial treatment. * Patients with untreated central nervous system metastases or local treatment of brain metastases within the last 6 months. Patients with stable brain metastasis for 6 months post-intervention are eligible. Subjects with chordoma will be eligible regardless of site of disease if other eligibility criteria are met. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to BN-Brachyury or other agents used in trial. History of allergic reaction to aminoglycoside antibiotics or egg products. * Serious or uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that, in the opinion of the investigator, would limit compliance with trial requirements. * Pregnant women. * HIV-positive patients.