ZAP-IT: ZN-c3 + Carboplatin + Pembrolizumab in mTNBC

Inclusion Criteria: * Participants must have histologically or cytologically confirmed invasive breast cancer, with either locally advanced or metastatic disease. Patients without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation. * Either the primary invasive tumor and/or the metastasis must be triple-negative, defined as: * Hormone-receptor poor, ER- and PR-negative, or staining present in ≤10% by immunohistochemistry (IHC) * HER2-negative: 0 or 1+ by IHC, or FISH\<2.0 * Participants must have at least one lesion that is not within a previously radiated field that is measurable per RECIST version 1.1. Bone lesions are not considered measurable by definition. See Section 11 for the evaluation of measurable disease. * Prior chemotherapy: Patients have received 1-3 prior chemotherapeutic regimen for metastatic breast cancer, one of which must have contained an antibody drug conjugate. Prior cytotoxic chemotherapy must be discontinued at least 14 days before initiation of protocol therapy in the study. The patient must also not have progressed on a prior platinum in the metastatic setting. Receipt of platinum in neo\\adjuvant setting is allowed, with a disease recurrence later than 6 months post platinum treatment end. * Prior biologic therapy: Patients must have discontinued all biologic therapy at least 14 days before treatment start date participation. * Prior immune checkpoint inhibitor is allowed. Patients with prior history of prior immune-related adverse events with immune checkpoint inhibitors will be excluded. * Prior radiation therapy: Patients may have received prior radiation therapy in either the metastatic or early-stage setting. Radiation therapy must be completed at least 14 days prior to study treatment initiation, unless given for palliation when 7 days is acceptable, and patients should have recovered from adverse effects of radiation to grade ≤1. * Age ≥ 18 * ECOG performance status ≤ 2 * Participants must have normal organ and marrow function as defined below: * ANC ≥1.5 × 109 /L (excluding measurements obtained within 7 days after administration of short-acting hematopoietic growth factors, or within 3 weeks after longacting hematopoietic growth factors). * Platelet count ≥100 × 109 /L (excluding measurements obtained within 3 days after transfusion of platelets or within 3 weeks after administration of platelet growth factor). * Hemoglobin ≥9.5 g/dL (excluding measurements obtained within 2 weeks after blood transfusion. * Serum creatinine ≤1.5 × upper limit of normal (ULN) or creatinine clearance (CrCl) ≥60 mL/min using the Cockcroft-Gault equation or by 24-hour urine collection test. * Total bilirubin (sum of conjugated + unconjugated) ≤1.5 × ULN or ≤3 × ULN in the case of Gilbert's disease. * ALT and AST ≤2.5 × ULN. If liver function abnormalities are due to underlying liver metastases: AST and ALT ≤3 × ULN. * Participants who are HBsAg positive are eligible if they have received HBV anti-viral therapy for at least 4 weeks and have undetectable HBV viral load prior to enrollment. * Note: Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention. --Hepatitis B screening tests are not required unless: * Known history of HBV infection * As mandated by local health authority * Participants with a history of HCV infection are eligible if HCV viral load is undetectable at screening. * Note: Participants must have completed curative anti-viral therapy at least 4 weeks prior to enrollment. * Hepatitis C screening tests are not required unless: * Known history of HCV infection * As mandated by local health authority * HIV-infected participants must have well-controlled HIV on ART, defined as: * Participants on ART must have a CD4+ T-cell count ≥350 cells/mm3 at the time of screening * Participants on ART must have achieved and maintained virologic suppression defined as confirmed HIV RNA level below 50 or the LLOQ (below the limit of detection) using the locally available assay at the time of screening and for at least 12 weeks before screening * It is advised that participants must not have had any AIDS-defining opportunistic infections within the past 12 months. * Participants on ART must have been on a stable regimen, without changes in drugs or dose modification, for at least 4 weeks before study entry (Day 1) and agree to continue ART throughout the study ---The combination ART regimen must not contain any antiretroviral medications that interact with CYP3A4 inhibitors/inducers/substrates (https://www.fda.gov/drugs/drug-interactions-labeling/drug-development-anddrug-interactions-table-substrates-inhibitors-and-inducers) * Patients who undergo an attempted on-treatment research biopsy and in whom inadequate tissue is obtained are still eligible to continue protocol therapy. * Clinical biopsy performed within the required time frame before enrollment can replace study biopsy if there is residual material (at least 10 FFPE tumor containing slides). * Female subjects of childbearing potential must have a negative serum pregnancy test at screening. This must be performed or repeated within 72h of treatment start. * The effects of azenosertib on the developing human fetus are unknown. Women of childbearing potential and men must agree to use adequate methods of contraception. All women are considered to be of childbearing potential unless they fulfill one of the following criteria at screening: * Post-menopausal defined as age ≥50 and amenorrheic for at least 12 months * Women age \<50 if they have been amenorrheic for at least 12 months and have a serum follicle-stimulating hormone (FSH) and luteinizing hormone (LH) level in the postmenopausal range (per institutional standards). * Documentation of irreversible surgical sterilization by hysterectomy, bilateral oophorectomy, or bilateral salpingectomy, or bilateral tubal ligation * Appropriate contraception should be used throughout the duration of study participation, and for six months after the last dose of azenosertib or 120 days (5 half-lives) after the last dose of pembrolizumab, whichever comes last. Acceptable methods of contraception include abstinence, tubal ligation, intra-uterine devices, and vasectomized partner. Additionally, male patients should refrain from donating sperm from the start of dosing until 6 months after discontinuing azenosertib. If male patients wish to father children they should be advised to arrange for freezing of sperm samples prior to the start of study treatment. * Participant must be able to swallow pills. * Ability to understand and the willingness to sign a written informed consent document. * Patients with a history of treated central nervous system (CNS) metastases are eligible. Treated brain metastases are defined as those having no evidence of progression for ≥ 1 month after treatment, or hemorrhage for \>/= 2 weeks after treatment and no ongoing requirement for corticosteroids, as ascertained by clinical examination and brain imaging (magnetic resonance imaging or CT scan) during the screening period. Any corticosteroid use for brain metastases must have been discontinued without the subsequent appearance of symptoms for ≥2 weeks before the first study drug. Treatment for brain metastases may include whole brain radiotherapy, radiosurgery, or a combination as deemed appropriate by the treating physician. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. Exclusion Criteria: * Major surgical procedures \<28 days from treatment start date. * Participants who have received a prior inhibitor of WEE1 kinase activity. * Participants who have progressed on prior platinum chemotherapy. Patients who received prior pembrolizumab and carboplatin are eligible as long as they didn't progress while on this regimen. Patients who received pembrolizumab and other non-platinum chemotherapy are eligible, even if they progressed on this regimen. * Known brain metastases that are untreated, symptomatic, or require therapy to control symptoms. Patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 1 month before day 1 of study treatment will be excluded. * Patients with current residual grade ≥2 neuropathy or grade ≥2 toxicity (except alopecia or anorexia) from prior therapy. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to azenosertib, carboplatin or pembrolizumab. * Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients. * Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Participant may not have a percutaneous endoscopic gastrostomy (PEG) tube or be receiving total parenteral nutrition (TPN). * Has received an investigational agent or has used an investigational device within 4 weeks prior to study intervention administration. * Has received a live vaccine or live-attenuated vaccine within 30 days before the first dose of study intervention. Administration of killed vaccines is allowed. * Known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ, excluding carcinoma in situ of the bladder, that have undergone potentially curative therapy are not excluded. Participants with low risk early-stage prostate cancer (T1-T2a, Gleason score ≤6, and PSA \<10 ng/mL) either treated with definitive intent or untreated in active surveillance with stable disease are not excluded. * Participants receiving any medications, substances, or foods (ie, grapefruit juice) listed below are ineligible (Please refer to Section 5.6 for list of restricted co-medications): --Concurrent treatment with drugs or foods that are strong or moderate cytochrome P450 (CYP)3A4/ CYP3A5 inhibitors or P-gp inhibitors or strong or moderate CYP3A4/CYP3A5 inducers, strong CYP3A4/CYP3A5 inhibitors should be discontinued before five half-lives, and CYP3A4/CYP3A5 inducers should be discontinued 14 days prior to the first dose of the study drugs. * Participants who have an uncontrolled intercurrent illness, including, but not limited to, ongoing or active infection, uncontrolled hypertension, unstable angina pectoris, uncontrolled cardiac arrhythmia, congestive heart failure-New York Heart Association Class III or IV (Appendix B), active ischemic heart disease, myocardial infarction within the previous six months, uncontrolled diabetes mellitus, gastric or duodenal ulceration diagnosed within the previous 6 months, chronic liver or renal disease, or severe malnutrition. In addition, patients are ineligible if they have a psychiatric illness or a social situation that could limit their ability to comply with the study requirements. * Participants who have refractory nausea and vomiting, chronic gastrointestinal diseases, or previous significant bowel resection that would preclude adequate absorption of azenosertib. * Participant with mean resting corrected QT interval (specifically QTc calculated using the Fridericia formula \[QTcF\]) 470 msec, on baseline ECG, or congenital long QT syndrome. * History or current evidence of congenital or family history of long QT syndrome or Torsade de Pointes (TdP). * Taking medications with a known risk of TdP. * Concomitant medication that leads to significant QT prolongation * Has an active infection or active TB requiring systemic therapy. * Has active autoimmune disease that has required systemic treatment in the past 2 years except replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid) * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (i.e., dosing exceeding 10 mg daily of prednisone or equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment. * Has not adequately recovered from major surgery or has ongoing surgical complications. * Has a history or current evidence of any condition, therapy, or laboratory abnormality or other circumstance that might confound the results of the study, interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. * Has had an allogenic tissue/solid organ transplant.