This phase Ib/II trial studies the side effects and best dose of olaparib and vistusertib (AZD2014) or olaparib and capivasertib (AZD5363) when given together in treating patients with endometrial, triple negative breast cancer, ovarian, primary peritoneal, or fallopian tube cancer that has come back (recurrent). Olaparib, vistusertib, and capivasertib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

PRIMARY OBJECTIVES:

I. To determine the maximally tolerated dose (MTD) and recommended phase II dose (RP2D) of the combinations of AZD2014 + olaparib and confirmation of recommended phase 2 dose (RP2D) for the AZD5363 + olaparib combination in patients with recurrent endometrial, recurrent triple negative breast, recurrent high-grade serous ovarian, or recurrent breast cancer, BRCA mutant ovarian cancer.

SECONDARY OBJECTIVES:

I. To determine the tolerability of the RP2D of AZD2014 + olaparib and AZD5363 + olaparib.

II. To determine the safety and observed toxicities of the combination of AZD2014 + olaparib and AZD5363 + olaparib in patients with recurrent endometrial, recurrent triple negative breast, recurrent high-grade serous ovarian, or BRCA mutant ovarian cancer.

III. To estimate the activity of these drug combinations at all dose levels in each patient cohort by objective response rate and proportion of patients surviving progression free (PFS) at 6 months.

IV. To determine response duration of these combinations at all dose levels. V. To determine the pharmacokinetics (PK) of each agent alone and in combination to assess the presence of any drug interaction between the two co-administered agents.

EXPLORATORY TRANSLATIONAL OBJECTIVES:

I. To determine if response to therapy is associated with molecular profile of the tumor (including, but not limited to, molecular aberrations in the phosphoinositide-3-kinase [PI3K]- v-akt murine thymoma viral oncogene homolog [AKT]- mechanistic target of rapamycin [mTOR] pathway or defects in homologous recombination) before treatment.

II. To examine associations with early changes in functional proteomic biomarkers in tumor biopsies before and after treatment and tumor response in patients with recurrent endometrial, recurrent triple negative breast, recurrent high-grade serous ovarian, or BRCA mutant ovarian cancer treated with the investigational agents.

III. To determine the molecular profile of unusual responders (significant regression of disease or progression of disease).

IV. To provide data to investigate the relationship between plasma concentrations/exposure and changes in safety and efficacy outputs to facilitate population analysis by sponsor.

OUTLINE: This is a dose-escalation study. Patients are assigned to 1 of 3 treatment arms.

ARM I (CONTINUOUS AZD2014 DOSING): Patients receive olaparib orally (PO) twice daily (BID) on days 1-28 (days 5-28 of course 1 and alone on days -3 to -1 of week -1) and vistusertib PO BID on days 1-28 (alone on days 1-4 of week 1).

ARM II (INTERMITTENT AZD2014 DOSING): Patients receive olaparib PO BID on days 1-28 (days 3-28 on course 1 and alone on days -5 to -3 of week -1) and vistusertib PO BID for 2 days on and 5 days off (alone on days 1-2 of week 1).

ARM III (INTERMITTENT AZD5363 DOSING): Patients receive olaparib PO BID on days 1-28 (on days 5-28 of course 1 and alone on days -3 to -1 of week -1) and capivasertib PO BID for 4 days on and 3 days off (alone on days 1-4 of week 1).

In all arms, courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up within 4 weeks.

Inclusion Criteria:

• Any histologically confirmed locally advanced recurrent endometrial adenocarcinoma (except for carcinosarcoma), recurrent high-grade serous ovarian/primary peritoneal/fallopian tube carcinoma, or deleterious BRCA mutant recurrent ovarian/primary peritoneal/fallopian tube cancer for whom no curative option is available will be eligible; any patient proven to have metastatic triple negative breast cancer, defined from standard pathologic assays as negative for estrogen receptor (ER) and progesterone receptor (PR) (< 10% tumor staining) will be eligible
• Patients may have unlimited prior chemotherapeutic regimens for management of recurrent locally advanced endometrial carcinoma, recurrent ovarian carcinoma, or metastatic triple negative breast cancer; treatment as frontline therapy for metastatic disease is acceptable; patients who have received prior PARP inhibitors, MTOR inhibitors, and/or AKT inhibitors are allowed to participate; patients may have progressed on prior PARP inhibitor, MTOR inhibitor, or AKT inhibitor but they may not have discontinued drug for toxicity
• With the exception of alopecia, any unresolved toxicities from prior chemotherapy should be no greater than Common Terminology Criteria for Adverse Events (CTCAE) (version 4.0) grade 1 at the time of starting study treatment
• Patients should have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; if no measurable disease is present, patients should have assessable disease such as pleural effusion, ascites, with cancer antigen 125 (CA125) Gynecological Cancer Intergroup (GCIG) criteria
• Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
• Women of child-bearing potential and their partners must agree to use contraception (hormonal or barrier method of birth control; abstinence) from study entry until 30 days after last dose of study drug; male partners should be instructed to use contraception during the study period; women of child-bearing potential (intact uterus) should have a negative serum pregnancy test; if a woman becomes pregnant or suspects she is pregnant while on study, she should tell her treating physician immediately; female patients must have evidence of non-child-bearing potential by fulfilling 1 of the following at screening: a) post-menopausal defined as > 50 years old and amenorrheic for >= 12 consecutive months following cessation of all exogenous hormonal treatments; b) documentation of irreversible surgical sterilization by hysterectomy, bilateral oophorectomy or bilateral salpingectomy, but not tubal ligation
• Women must not breast-feed while taking the study medications
• Absolute neutrophil count >= 1,500/mcL (measured within 28 days prior to entry/randomization)
• Hemoglobin >= 10 gm/dL (measured within 28 days prior to entry/randomization)
• Platelets >= 100,000/mcL (measured within 28 days prior to entry/randomization)
• Presence of < 4% blasts on hematologic studies (measured within 28 days prior to entry/randomization)
• Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (measured within 28 days prior to entry/randomization)
• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 2.5 x upper limit of normal unless the liver is involved with tumor, in that case, ALT/AST must be =< 5 x ULN (measured within 28 days prior to entry/randomization)
• Creatinine clearance > 50 mL/min (assessed by Cockcroft Gault estimation) (measured within 28 days prior to entry/randomization)
• Patients with type II diabetes mellitus that is well controlled by dietary measures alone and have a hemoglobin A1c (HgA1c) < 8% are eligible to participate; patients found to have a fasting glucose >= 7 mmol/L (>= 126 mg/dL) or glycosylated hemoglobin > 8% (64 mmol/mol) at screening should be assessed for appropriate management according to local policy; those in whom dietary measures alone provide good diabetic control will be eligible for inclusion; type I or II diabetes mellitus requiring either insulin or oral hypoglycemics for routine management will be excluded
• Patients must be able to swallow and tolerate oral medications and not have gastrointestinal illnesses that would preclude absorption of AZD2014, AZD5363, or olaparib (e.g. uncontrolled nausea, vomiting, or diarrhea; malabsorption syndrome; ulcerative disease)
• Participants' life expectancy must be > 4 months
• Patients must be able to understand and willing to sign an informed consent
• FOR EXPANSION PHASE ONLY: For the expansion phase, patients must have measurable disease accessible for biopsy
• FOR EXPANSION PHASE ONLY: For the expansion phase, patients must have archival specimens from the time of primary or recurrence diagnosis

Exclusion Criteria:

• Patients receiving any other investigational agents or any additional anti-cancer agents
• Patients who have endometrial carcinosarcoma; patients with ovarian cancer who have histology other than high-grade serous in the absence of a deleterious BRCA mutation; if the patient has a deleterious BRCA mutation, any histology will be accepted
• Patients who have recurrences that are amenable to potentially curative treatment with radiation therapy or surgery
• Patients who have a history of other malignancies except for basal cell or squamous cell skin cancer, in situ cervical cancer, unless they have been disease-free for at least five years; patients may have dual primaries of endometrial, ovarian or breast cancer
• Patients who have a history of myelodysplastic syndrome
• Patients who have symptomatic, uncontrolled spinal cord compression and/or brain metastases; a scan to confirm absence of brain metastasis is not required; patients can receive a stable dose of corticosteroids (except those prohibited per protocol) before/during study if these were started at least 28 days prior to entry
• Patients who have had prior chemotherapy, biological therapy, radiation therapy, androgens, thalidomide, immunotherapy, other anticancer agents, and any investigational agents within 28 days of starting study treatment (not including palliative radiotherapy at focal sites), or corticosteroids that are prohibited per protocol within 14 days of starting study treatment
• Patients who have had major surgery within 28 days prior to entry into the study or be recovering from any effects of surgery; patients who have had minor surgery within 2 weeks prior to entry into the study
• Patients who have a resting electrocardiogram (ECG) with a Fridericia corrected QT (QTcF) interval of >= 470 msec at 2 or more time points within a 24 hour period or a family history of long QT syndrome
• Patients who have required a blood transfusion within 28 days prior to study start
• Patients who have received any hemopoietic growth factors (e.g., filgrastim [G-CSF], sargramostim [GM-CSF]) within 2 weeks prior to study start
• Patients receiving certain medications and/or substances that are prohibited within stated wash-out periods
• Patients with known hypersensitivity to olaparib, AZD5363, AZD2014 or any of their excipients; patients with a history of hypersensitivity to drugs with a similar chemical structure or class to olaparib, AZD5363, or AZD2014
• Patients who have experienced intolerable adverse events per treating investigator due to other PARP inhibitors, mTOR inhibitors, PI3 kinase inhibitors, or AKT inhibitors
• Patients who have experienced any of the following procedures or conditions currently or in the preceding 12 months: a) coronary artery bypass graft; b) angioplasty; c) vascular stent; d) myocardial infarction; e) angina pectoris; f) congestive heart failure New York Heart Association grade >= 2; g) ventricular arrhythmias requiring continuous therapy; h) supraventricular arrhythmias including atrial fibrillation, which are uncontrolled; i) hemorrhagic or thrombotic stroke, including transient ischemic attacks or any other central nervous system bleeding
• Patients who have abnormal echocardiogram (ECHO) or multi-gated acquisition scan (MUGA) at baseline (left ventricular ejection fraction [LVEF] < 50%); appropriate correction to be used if a MUGA is performed
• Patients with torsades de pointes within 12 months of study entry
• Patients with uncontrolled hypotension (systolic blood pressure < 90 mmHg and/or diastolic blood pressure < 50 mmHg)
• Patients with proteinuria (3+ on dipstick or 300 mg/dL on urine analysis or > 500 mg/dL/24 hours)
• Patients with diabetes type I or uncontrolled type II (HbA1c > 8 % assessed locally) as judged by the investigator
• As judged by the investigator, any evidence of severe or uncontrolled systemic diseases (e.g., severe hepatic impairment, interstitial lung disease [bilateral, diffuse, parenchymal lung disease], uncontrolled chronic renal diseases [glomerulonephritis, nephritic syndrome, Fanconi syndrome or renal tubular acidosis]), or current unstable or uncompensated respiratory or cardiac conditions, or uncontrolled hypertension (blood pressure >= 140/90), active bleeding diatheses or active infection including hepatitis B, hepatitis C, and human immunodeficiency virus; screening for chronic conditions is not required
• As judged by the investigator, the patient is unsuitable to participate in the study and the patient is unlikely to comply with study procedures, restrictions, and requirements
• FOR EXPANSION PHASE ONLY: Lack of accessible tumor for biopsy
• Lack of archival specimens from the time of primary or recurrence diagnosis