Pomalidomide and Nivolumab in People With Virus-Associated Malignancies With or Without HIV

Background: Less toxic and more effective treatments are needed for cancers caused by viruses. These cancers include Hodgkin and non-Hodgkin lymphoma, hepatocellular carcinoma, head and neck cancer, nasopharyngeal carcinoma, gastric cancer, anal cancer, cervical cancer, vaginal cancer, vulvar cancer, penile cancer, Merkel cell carcinoma, Kaposi sarcoma, and leiomyosarcoma. Researchers want to see if a combination of drugs can help. Objective: To find a safe dose of pomalidomide plus nivolumab in people with cancers caused by viruses. Eligibility: Adults ages 18 or older who have cancers caused by Epstein Barr virus (EBV), human herpes virus 8/Kaposi sarcoma herpesvirus (HHV8/KSHV), human papilloma virus (HPV), hepatitis B or C virus (HBV/HCV), and Merkel cell polyomavirus (MCPyV) that have not responded to previous treatments or have relapsed, or in adults who do not want to have surgery because of disfigurement or other risks. Adults who have HIV with any CD4 T cell count are eligible. Design: Participants will be screened with blood and urine tests, scans, and heart tests. They will have a physical exam. Their ability to perform normal daily activities will be assessed. They may have a tumor biopsy. Treatment will be given in 28-day cycles. Participants will take pomalidomide as a tablet by mouth for 21 days of each cycle, for up to 24 cycles. They will get nivolumab by intravenous infusion once each cycle. They will take an aspirin each day until 30 days after their last dose of the study drugs. Participants will keep a pill diary. They will bring it to their study visit at the end of each cycle. At these visits, some screening tests will be repeated. Participants with Kaposi sarcoma will have pictures taken of their lesions. Participants will give blood and saliva samples for research. They may have optional anal and/or cervical swabs. They may have optional biopsies. Participants will have a follow-up visit 30 days after they stop taking the study drugs, then every month for 100 days. Some screening tests will be repeated. Then they may by contacted by phone every 3 months for 9 months, and then every 6 months thereafter.