This is an investigator initiated single institution, open-label study to evaluate the antitumor activity, safety, and tolerability of durvalumab in combination with tremelimumab in subjects with select advanced rare solid tumors. The dose-exploration phase, conducted across a range of tumor types, has been completed. The dose-expansion phase is ongoing and includes certain soft tissue sarcomas, neuroendocrine tumors and thymic carcinoma. Therefore, subjects diagnosed with any of those rare tumors are excluded from this trial. Given the safety and tolerability data in the previous and ongoing studies (Study D4190C00010 and D4190C00006), the selected dose for evaluation in all subjects enrolled in this trial is as follows: