This partially randomized phase I/II trial studies the side effects and the best dose of cediranib maleate and olaparib and to see how well they work compared to olaparib alone in treating patients with ovarian, fallopian tube, peritoneal, or triple-negative breast cancer that has returned after a period of improvement. Cediranib maleate may help keep cancer cells from growing by affecting their blood supply. Olaparib may stop cancer cells from growing abnormally. The combination of cediranib maleate and olaparib may help to keep cancer from growing.