AMTEC IIT: Phase 2 Multiarm Study in TNBC

Inclusion Criteria:

* Ability to understand and the willingness to sign a written informed consent document
* Participants are \>= 18 years old at time of informed consent.
* Metastatic TNBC, as defined by:

  * Estrogen receptor (ER) and progesterone receptor (PR) negative as defined as ER \< 10% and PR \< 10% by immunohistochemistry according to American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines for hormone receptor testing
  * HER2 non-amplified per ASCO/CAP guidelines, defined as:

    * IHC score 0/1+
    * IHC 2+ and in situ hybridization (ISH) non-amplified with a ratio of HER2 to CEP17 \< 2.0, and if reported, average HER2 gene copy number \< 4 signals/cells; or
    * ISH non-amplified with a ratio of HER2 to CEP17 \<2.0, and if reported, average HER2 gene copy number \< 4 signals/cells
* Participants with or without germline BRCA mutated TNBC are eligible for study participation
* Participants must have at least one measurable site of disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 that is amenable to biopsy
* Prior therapies for metastatic breast cancer

  * Frontline patients who have not received prior systemic therapy for metastatic breast cancer are eligible
  * Patients who have received =\< 2 prior chemotherapy regimens for metastatic breast cancer are eligible
* Participants must have fully recovered from the acute toxic effects of all prior treatment to grade 1 or less, except alopecia which is allowed
* Participants must have a life expectancy \>= 16 weeks
* Participant must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 1
* Participant must consent to undergo a pre-treatment screening biopsy for enrollment and subsequent biomarker analyses
* Participants must consent to undergo one mandatory on-study tumor biopsy following a 2-week induction treatment of olaparib. A second on-study biopsy at time of disease progression is optional, but not mandatory
* Participants must not have received previous treatment with PARP inhibitors, including olaparib
* Hemoglobin \>= 10.0 g/dL (measured within 28 days prior to administration of study treatment)
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (measured within 28 days prior to administration of study treatment)
* Platelet count \>= 100 x 10\^9/L (measured within 28 days prior to administration of study treatment)
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (measured within 28 days prior to administration of study treatment)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal unless liver metastases are present in which case they must be =\< 5 x ULN (measured within 28 days prior to administration of study treatment)
* Participants must have creatinine clearance estimated of \>= 51 mL/min using the Cockcroft-Gault equation or based on a 24 hour urine test (measured within 28 days prior to administration of study treatment)
* Participants of childbearing potential must have a negative urine or serum pregnancy test within 28 days of study treatment and confirmed on Day 1 prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Participants of childbearing potential agree to use adequate methods of contraception, upon signing of informed consent through:

  * 6 months after the last dose with olaparib,
  * 3 months after the last dose with durvalumab,
  * 1 week after the last dose with selumetinib,
  * 1 month after the last dose with capivasertib,
  * 1 month after the last dose with ceralasertib.
* Participants of childbearing potential are those who are not proven postmenopausal. Postmenopausal is defined as:

  * Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments
  * Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the post-menopausal range for women under 50
  * Radiation-induced oophorectomy with last menses \>1 year ago
  * Chemotherapy-induced menopause with \>1 year interval since last menses
  * Surgical sterilization (bilateral oophorectomy or hysterectomy)
* Sperm-producing participants must use a condom during treatment and for 3 months after the last dose of olaparib when having sexual intercourse with a pregnant partner or with an individual of childbearing potential. Partners of sperm-producing participants should also use a highly effective form of contraception if they are of childbearing potential

  * Sperm-producing participants assigned to receive capivasertib must use a condom during treatment and for 4 months after the last dose of capivasertib when having sexual intercourse with a pregnant partner or with an individual of childbearing potential

Exclusion Criteria:

* Any concurrent anticancer treatment

  * Individuals in the follow-up phase of a prior investigational study may participate as long as it has been 4 weeks since last dose of the previous investigational agent or device
  * Concurrent use of hormonal therapy for non-cancer related conditions (e.g., hormone replacement therapy) is allowed
* Participant's with tumors showing androgen receptor (AR) \>= 80% by immunohistochemistry are excluded
* Other malignancy unless curatively treated with no evidence of disease for \>= 5 years except: adequately treated non-melanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ (DCIS), stage 1, grade 1 endometrial carcinoma. Participants with a personal history of treated early stage breast cancer whose natural history or treatment does not have the potential to interfere with the safety or efficacy endpoints of the trial, per investigator assessment, are eligible
* Participants with myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML)
* Participant received prior anticancer therapy such as targeted therapies, or systemic chemotherapy or radiation (except for palliative reasons) within the past 3 weeks, or 5 half-lives, whichever is shorter, prior to first day of treatment
* Participants with known active central nervous system (CNS) metastases and/or carcinomatous meningitis

  * Patients with brain metastases may participate provided they do not have symptomatic uncontrolled disease. The patient can receive a stable dose of corticosteroids before and during the study as long as these were started at least 4 weeks prior to treatment. (note: a scan to confirm the absence of brain metastases is not required)
  * Patients with spinal cord compression are not eligible unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days
  * Patients with carcinomatous meningitis are not eligible
* Concomitant use of known strong CYP3A inhibitors (e.g., ketoconazole, posaconazole), or strong CYP3A inducers (e.g., phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). The required washout period prior to starting study intervention treatment is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents
* Major surgery within 4 weeks of starting study treatment and patients must have recovered from any effects of any major surgery
* Previous allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT)
* Patients that are immunocompromised, including those with human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness are not eligible for participation

  * Note: HIV-infected participants on effective anti-retroviral therapy with undetectable viral load for \>= 6 months are eligible for this trial provided that there is minimal interactions or overlapping toxicity of the antiretroviral therapy with their study intervention. Refer to drug-specific exclusion criteria for additional considerations
* Patients with known active hepatitis (i.e. hepatitis B or C). Refer to drug-specific exclusion criteria for additional considerations

  * Active hepatitis B virus (HBV) is defined by a known positive HBV surface antigen (HBsAg) result
  * Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody and absence of HBsAg) are eligible
  * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA. Those with a positive HCV PCR will be excluded
* Participants unable to swallow orally administered medication and participants with gastrointestinal disorders likely to interfere with absorption of the study medication
* Participants with visceral crisis defined as severe organ dysfunction as assessed by signs and symptoms, laboratory studies, and rapid progression of disease
* Active infection requiring systemic antibiotic therapy. Participants requiring systemic antibiotics for infection must have completed therapy before treatment is initiated
* Participants considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on high resolution computed tomography (HRCT) scan or any psychiatric illness/social situation that prohibits obtaining informed consent
* Resting electrocardiography (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (e.g., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, corrected QT interval by Fridericia's correction formula (QTcF) prolongation \> 500 ms, electrolyte disturbances, etc.), or participants with congenital long QT syndrome
* Participants with a history of hypersensitivity reactions to study agent, olaparib, or its excipients
* Participant is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment
* Sperm-producing participants are prohibited from donating sperm upon signing of informed consent through:

  * 3 months following last dose with olaparib
  * 4 months following last dose with capivasertib
  * 6 months following last dose with ceralasertib
* Involvement in the planning and/or conduct of the study
* Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements
* DRUG-SPECIFIC EXCLUSION CRITERIA: The following criteria require consideration for participant eligibility to one or more of the available treatment arms. Participant eligibility may be assessed at the time of initial screening or as part of the on-study assignment to a specific treatment arm
* DURVALUMAB EXCLUSION CRITERIA: Participant has received prior immunotherapy with anti-PD-L1, including durvalumab anti-PD-1, anti-CTLA4 or similar drugs in the metastatic setting
* DURVALUMAB EXCLUSION CRITERIA: Participants may have received prior immunotherapy in the adjuvant setting, provided

  * No documented disease progression on immunotherapy
  * Treatment with immunotherapy was \>1 year from enrollment on study
* DURVALUMAB EXCLUSION CRITERIA: Participant has evidence of interstitial lung disease or active non-infectious pneumonitis
* DURVALUMAB EXCLUSION CRITERIA: Major surgery within 2 weeks of starting study treatment and participants must have recovered from any effects of any major surgery

  * Note: Local surgery of isolated lesions for palliative intent is acceptable per investigator discretion
* DURVALUMAB EXCLUSION CRITERIA: Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis (TB) testing in line with local practice), hepatitis B (positive HBV surface antigen (HBsAg) result), hepatitis C, or human immunodeficiency virus

  * Participants with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible.
  * Participants positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA)
  * Those with controlled human immunodeficiency virus (HIV) are eligible, provided that:

    * Baseline CD4+ T-cell count is \>= 200 cells/mm\^3, and
    * HIV plasma viral load is \< 60 copies/ml
* DURVALUMAB EXCLUSION CRITERIA: History of active primary immunodeficiency
* DURVALUMAB EXCLUSION CRITERIA: Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid. The following are exceptions to this criterion:

  * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection)
  * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent
  * Steroids as premedication for hypersensitivity reactions (e.g., computed tomography (CT) scan premedication)
* DURVALUMAB EXCLUSION CRITERIA: Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.\]). The following are exceptions to this criterion:

  * Participants with vitiligo or alopecia
  * Participants with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement
  * Any chronic skin condition that does not require systemic therapy
  * Participants without active disease in the last 5 years may be included but only after consultation with the study physician
  * Participants with celiac disease controlled by diet alone
* DURVALUMAB EXCLUSION CRITERIA: History of allogenic bone marrow transplant or double umbilical cord blood transplantation
* DURVALUMAB EXCLUSION CRITERIA: Participants must not have received live vaccines within 30 days prior to the first dose of