Safety and Tolerability of a Modified Vaccinia Ankara (MVA)-Based Vaccine Modified to Express Brachyury and T-cell Costimulatory Molecules (MVA-Brachyury-TRICOM)

Background: \- This cancer vaccine was developed to help teach the body's immune system to attack and destroy cancer cells. It teaches immune cells to target the Brachyury protein. This protein is present in some tumor cells, and it can help tumor cells spread to other parts of the body. Researchers want to see whether the new Brachyury protein vaccine can help treat people with advanced carcinomas. Objective: \- To test the safety and effectiveness of giving the modified vaccinia Ankara (MVA)-brachyury-B7-1, ICAM-1 (Intercellular Adhesion Molecule 1), and LFA-3 (lymphocyte function-associated antigen 3) TRICOM vaccine to people with cancer. Eligibility: \- Adults ages 18 and over whose type of cancer has not responded to standard therapies who do not have a history of autoimmune diseases and are capable of taking care of themselves. Design: * Participants will be screened with a medical history and physical exam. They will have blood and urine tests. They may have a computed tomography (CT) scan, a positron emission tomography (PET) scan, and a brain magnetic resonance imaging (MRI) scan. They may have a bone scan. They will have an electrocardiogram (ECG) to test heart rhythm. * Participants will have visits about every 4 weeks. They will have a physical exam and blood and urine tests. They will be injected with the vaccine under the skin into the upper thigh or around the armpits. * CT scans or MRI scans will be done at visit 1, after 3 months on study, and again 3 months later if still on the study. Another ECG will be done at their last vaccine visit. * When participants stop the vaccine, they will return for visits until they recover from any side effects. They will have tests including physical exam, blood tests, scans, and x-rays. * Participants will be asked to enroll in another study for long-term follow-up.