Cediranib Maleate and Olaparib in Treating Patients With Recurrent Ovarian, Fallopian Tube, or Peritoneal Cancer or Recurrent Triple-Negative Breast Cancer

Inclusion Criteria: * PHASE I: Participants must have histologically or cytologically confirmed epithelial ovarian cancer, primary peritoneal serous cancer, fallopian tube cancer, or triple-negative breast cancer * PHASE II: Participants must have histologically or cytologically grade 2 or 3 (high-grade) papillary-serous or endometrioid epithelial ovarian cancer, primary peritoneal serous cancer, or fallopian tube cancer; participants with epithelial ovarian, primary peritoneal, or fallopian tube cancers of other high-grade histologies who carry a known deleterious breast cancer gene (BRCA) germline mutation by standard clinical testing (Myriad BRAC Analysis) will also be considered eligible * PHASE I-T: Participants must have histologically or cytologically confirmed epithelial ovarian cancer, primary peritoneal serous cancer, or fallopian tube cancer * Ovarian cancer, primary peritoneal, and fallopian tube participants in the Phase 1 and Phase 1-T portions of this trial must have either measurable cancer by RECIST 1.1 criteria or an elevated cancer antigen (CA)125 level at least twice the upper limit of normal on two separate occasions at least 1 day but not more than 3 months apart; at least one of the samples should be within 1 week of starting treatment; patients with both an elevated CA125 and measurable cancer will be followed by RECIST 1.1 criteria; patients with only an elevated CA125 level will be followed by modified Gynecologic Cancer Intergroup (GCIG) criteria *…