Mesothelin-Targeted Immunotoxin LMB-100 in Combination With SEL-110 in Subjects With Malignant Pleural or Peritoneal Mesothelioma

Background: Mesothelioma is cancer of the tissue that lines some organs. A new drug, LMB-100, may bind to a protein on mesothelioma tumors and kill cancer cells. But sometimes the body makes antibodies that reduce how well LMB-100 works. Researchers want to see if adding the drug SEL-110 to LMB-100 will prevent these antibodies from forming. Objective: To learn how safe and tolerable LMB-100 plus SEL-110 is in people with advanced mesothelioma. Eligibility: Adults ages 18 and older who have pleural or peritoneal mesothelioma that has not responded to prior platinum-based therapy Design: Participants will be screened with * Medical history * Physical exam * Blood and urine tests * Sample of tumor tissue. This can be from a previous procedure. * Scan of the chest, abdomen, and pelvis. Participants will lie on a table in a scanner that takes pictures. A special dye may be injected in a vein. * Positron emission tomography (fludeoxyglucose positron emission tomography (FDG-PET)) scan. A sugar attached to a chemical that gives off a signal will be injected before the scan. * Heart function tests The study will be done in 21-day cycles. Participants will get the study drugs for up to 4 cycles. They will get them through an intravenous (IV) catheter (a tube inserted in a vein, usually in the arm): * LMB-100 for about 30 minutes on day 1, day 3, and day 5 of each cycle * SEL-110 for about 1 hour on day 1 of each cycle Participants will get standard medicines to help prevent side effects. Participants will repeat some screening tests during each cycle and about 5 weeks after the last dose of study drug.