Olaparib, Durvalumab, and Tremelimumab in Treating Patients With Recurrent or Refractory Ovarian, Fallopian Tube or Primary Peritoneal Cancer With BRCA1 or BRCA2 Mutation

Patients must have platinum-sensitive or platinum-resistant recurrent or persistent or refractory ovarian, fallopian tube, or primary peritoneal carcinoma AND have one or more of the following characteristics documented on a validated platform (documented genetic test report is required). Historic report is permitted.

A germline BRCA1 or BRCA2 deleterious alteration.

A somatic mutation in BRCA1 or BRCA2 detected in a tumor sample or on circulating tumor DNA

Carry a known or likely loss of function alteration in one or more of the homologous recombination or mismatch repair pathways genes

Demonstrate a genomic phenotype of HR deficiency as measured by a LOH-high score.

* Recurrent ovarian cancer is defined as recurrence of disease in a patient who achieved initial complete response to primary therapy

* Persistent ovarian cancer is defined as having residual disease in the form of elevated tumor markers or microscopic or clinically evident disease in a patient who has completed and apparently responded to initial chemotherapy

* Refractory ovarian cancer is defined as patients who have failed to achieve at least a partial response to therapy including patients with either stable disease or disease progression during primary therapy

* Platinum-sensitive is defined as achievement of documented response to initial platinum-based treatment and has been off treatment for an extended period of time (more than 6 months)

* Platinum-resistant is defined as relapse within 6 months of last platinum-based chemotherapy or progression while on platinum-based therapy

All patients must have measurable disease as defined by immune-related Response Evaluation Criteria in Solid Tumors (irRECIST); measurable disease is defined as 10 mm in the longest diameter by computed tomography (CT) or magnetic resonance imaging (MRI) scan (or no less than double the slice thickness) for non- nodal lesions and \>= 15 mm in short axis for nodal lesions, 20 mm by chest X-ray, a lymph node must be \>= 15 mm in short axis when assessed by CT scan (CT scan slice thickness recommended to be no greater than 5 mm)

Must have archival tissue available for PD-L1 assessment

Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\])

Patients who have the following risk factors are considered to be at increased risk for cardiac toxicities and may be enrolled only with increased monitoring: i) prior treatment with anthracyclines; ii) prior treatment with trastuzumab; iii) a New York Heart Association classification of II controlled with treatment; iv) prior central thoracic radiation therapy (RT), including RT to the heart

Any hormonal therapy being taken as a treatment for cancer must be discontinued at least one week prior to registration; continuation of hormone replacement therapy e.g. thyroid hormone replacement therapy is permitted

Able to tolerate oral medications and no GI illnesses that would preclude absorption of olaparib

Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1

Life expectancy of \> 6 months

Hemoglobin \>= 10 g/dL (no blood transfusion in the 28 days prior to entry \[olaparib guidelines\])

White blood cell count (WBC) \> 3 x 10\^9/L

Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (\>=1500 per mm\^3)

Platelet count \>= 100 x 10\^9/L (\>= 100,000 per mm\^3)

Serum bilirubin =\< 1.5 x institutional upper limit of normal (ULN); this will not apply to subjects with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician

Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal unless liver metastases are present, in which case it must be =\< 5 x ULN

Creatinine =\< 1.5 x ULN, serum creatinine clearance (CL) \> 51 ml/min (by the Cockcroft- Gault equation)

Female subjects must either be of non-reproductive potential (i.e., post-menopausal by history: \>= 60 years old and no menses for \>=1 year without an alternative medical cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative serum pregnancy test within 28 days of study treatment, confirmed prior to treatment on day 1

Participants of child-bearing potential must agree to use two highly effective and acceptable forms of contraception from screening, throughout their participation in the study and for 180 days after the last dose of durvalumab + tremelimumab combination therapy or 90 days after last dose of durvalumab or olaparib, whichever is the longer time period (e.g., hormonal or barrier method of birth control); should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately

Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure

Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up

What this study is about