Bintrafusp Alfa (M7824) in Subjects With Thymoma and Thymic Carcinoma

Background: Thymoma and thymic carcinoma are diseases of the thymus. Platinum-based chemotherapy is the standard treatment for these diseases. But in many cases, the disease returns after treatment. Researchers want to see if a new drug can help. Objective: To see if bintrafusp alfa (M7824) is an effective treatment for thymoma and thymic carcinoma. Eligibility: People age 18 and older who have thymoma or thymic cancer and their disease returned or progressed after treatment with at least one platinum-containing chemotherapy treatment plan. Design: Participants will be screened under a separate protocol. Their medical, medicine, and treatment history will be reviewed. They will have a tumor biopsy if they do not have a sample. Participants will get the study drug once every 2 weeks as an intravenous infusion. For this, a small plastic tube is put into an arm vein. During the study, participants will undergo the following: Medicine review Physical exam Review of their symptoms and their ability to perform their normal activities Blood and urine tests Thigh muscle scan (using MRI) Tumor assessment (using MRI or CT) Heart and lung function tests Thyroid gland test Skin assessment. Participants may have tumor biopsies. Some of their blood and biopsy samples will be used for gene testing. Participants may take the study drug until their disease worsens or they cannot tolerate treatment. Participants will have follow-up visits 2 and 6 weeks after stopping treatment. Then they will have long-term follow-up visits every 3 months. These may include imaging scans. Visits may be done by phone, with scans (if needed) done at their doctor's office.

* IINCLUSION CRITERIA: * Participants must have histologically confirmed (by the pathology department/CCR/NCI) thymoma or thymic carcinoma. * Participants must have had at least one prior line of platinum-based chemotherapy. Progressive disease must be documented prior to study entry and participants must have advanced, unresectable disease that is not amenable to surgical resection. * Disease must be measurable with at least 1 unidimensional measurable lesion by RECIST1.1. * Participants must be aged \>=18 years. * ECOG performance status \= 1,500/mm\^3 OR \>= 1.5 x 10\^9/L * platelets: \>=\> 100,000/mm\^3 OR \>= 100 x 10\^9/L * hemoglobin: \>= 9g/dL (may have been transfused) * total bilirubin: \