Patients receive olaparib orally (PO) twice daily (BID), and tremelimumab intravenously (IV) over 1 hour and durvalumab IV over 1 hour on day 1. Treatment with olaparib continues for up to 12 months in the absence of disease progression or unacceptable toxicity. Treatment with tremelimumab repeats every 4 weeks for up to 4 courses and treatment with durvalumab repeats every 4 weeks for up to 13 courses in the absence of disease progression or unacceptable toxicity.