A Randomized Phase II/III Study of the Combination of Cediranib and Olaparib Compared to Cediranib or Olaparib Alone, or Standard of Care Chemotherapy in Women With Recurrent Platinum-Resistant or -Refractory Ovarian, Fallopian Tube, or Primary Peritoneal Cancer (COCOS)

• Patients must have histologically or cytologically confirmed ovarian cancer, peritoneal cancer or fallopian tube cancer and must have a histological diagnosis of either serous or endometrioid cancer based on local histopathological findings; both endometrioid and serous histology should be high-grade for eligibility of non-mutation carriers; patients with clear cell, mixed epithelial, undifferentiated carcinoma, or transitional cell carcinoma histologies are also eligible, provided that the patient has a known deleterious germline BRCA1 or BRCA2 mutation identified through testing at a clinical laboratory

⁃ Note: Due to the long acceptance of BRCA testing through Myriad, Myriad testing will be accepted; if testing for BRCA is done by other organizations, documentation from a qualified medical professional (e.g., ovarian cancer specialty physician involved in the field, high risk genetics physician, genetics counselor) listing the mutation and confirming that the laboratory results showed a recognized germ line deleterious BRCA 1 or BRCA 2 mutation or BRCA rearrangement is required (12/05/2016); a copy of Myriad or other BRCA mutational analysis (positive or variants of unknown significance \[VUS\] or negative) reports will be requested but not required for study enrollment

• Patients should have recurrent platinum-resistant or- refractory disease - defined as disease that has progressed by imaging while receiving platinum or had recurrence within 6 months of the last receipt of platinum-based chemotherapy; rising CA125 only is not considered as platinum-resistant or refractory disease (12/05/2016)

• Phase II study: measurable disease by RECIST 1.1 criteria; if archival tumor sample is not available tumor sample from fresh biopsy is acceptable (12/05/2016)

• Phase III study: evaluable disease - defined as RECIST 1.1 measurable disease OR non-measurable disease (defined as solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definitions for target lesions OR ascites and/or pleural effusion that has been pathologically demonstrated to be disease-related in the setting of a cancer antigen \[CA\]125 \>= 2 x upper limit of normal \[ULN\])

• No more than 3 prior treatment regimens (including primary therapy; no more than 1 prior non-platinum based therapy in the platinum-resistant/-refractory setting); hormonal therapies used as single agents (i.e. tamoxifen, aromatase inhibitors) will not count towards this line limit (12/05/2016)

• Patients may not have had a prior anti-angiogenic agent in the recurrent setting; prior use of bevacizumab in the upfront or upfront maintenance setting is allowed

• Patients may not have previously received a PARP-inhibitor

• Patient must have provided study specific informed consent prior to study entry

• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 or 2

• Absolute neutrophil count \>= 1,500/mcL (12/05/2016)

• Platelets \>= 100,000/mcL (12/05/2016)

• Hemoglobin \>= 10 g/dL (12/05/2016)

• Total bilirubin within =\< 1.5 times the upper limit of normal (ULN) institutional limits (12/05/2016)

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN; if intrahepatic liver metastases are present, AST and ALT must be =\< 5 times institutional ULN (12/05/2016)

• Creatinine =\< 1.5 x the institutional ULN (12/05/2016)

• Urine protein: creatinine ratio urine protein creatinine (UPC) of =\< 1 OR less than or equal to 2+ proteinuria on two consecutive dipsticks taken no less than 1 week apart; UPC is the preferred test; patients with 2+ proteinuria on dipstick must also have a 24-hour urine collection demonstrating protein of =\< 500 mg over 24 hours (12/05/2016)

• Toxicities of prior therapy (excepting alopecia) should be resolved to less than or equal to grade 1 as per CTCAE; patients with long-standing stable grade 2 neuropathy may be considered after discussion with the study chair.

• Adequately controlled blood pressure (systolic blood pressure \[SBP\] =\< 140; diastolic blood pressure \[DBP\] =\< 90 mmHg) on maximum of three antihypertensive medications; patients must have a BP of =\< 140/90 mmHg taken in the clinic setting by a medical professional within 2 weeks prior to starting study; it is strongly recommended that patients who are on three antihypertensive medications be followed by a cardiologist or a primary care physician for management of BP while on protocol; patients must be willing and able to check and record daily blood pressure readings; blood pressure cuffs will be provided to patients randomized to cediranib alone and the combination of olaparib and cediranib arms (12/05/2016)

• Adequately controlled thyroid function, with no symptoms of thyroid dysfunction and thyroid-stimulating hormone (TSH) within normal limits (12/05/2016)

• Able to swallow and retain oral medications and without gastrointestinal (GI) illnesses that would preclude absorption of cediranib or olaparib

• Age \>= 18 years

• Cediranib has been shown to terminate fetal development in the rat, as expected for a process dependent on VEGF signaling; for this reason, women of child-bearing potential must have a negative pregnancy test prior to study entry; women of child-bearing potential must agree to use two reliable forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 6 weeks after cediranib discontinuation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately

• Olaparib adversely affects embryofetal survival and development in the rat; for this reason, women of child-bearing potential must have a negative pregnancy test prior to study entry; women of child-bearing potential must agree to use must agree to use two reliable forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 3 months after the last dose of olaparib; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately