TAK-228 and TAK-117 Followed by Cisplatin and Nab Paclitaxel for Metastatic Triple Negative Breast Cancer

Inclusion Criteria: 1. Female patients 18 years or older. 2. Have a diagnosis of metastatic TNBC previously treated with standard anthracycline, cyclophosphamide, and taxane chemotherapy, unless there was a contraindication to doxorubicin, in which case prior treatment with this agent is not required. 3. Have not received more than 3 prior chemotherapy regimens for metastatic disease. Prior platinum and/or taxane therapy in the adjuvant or metastatic setting is permitted. 4. Androgen receptor-negative (less than 10% positive nuclei) on standard IHC performed at the local pathology laboratory. 5. Have locoregional (eg, breast, chest wall, regional lymphatic) or pulmonary or hepatic metastatic disease that is amenable to core needle biopsy. 6. Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 (See Appendix I) 7. Female patients who: 1. Are postmenopausal for at least 1 year before the screening visit, OR 2. Are surgically sterile, OR 3. If they are of childbearing potential, agree to practice 1 effective methods of contraception and 1 additional effective (barrier) method, at the same time, from the time of signing the informed consent through 90 days (or longer as mandated by local labeling \[eg, USPI, SmPC, etc,\]) after the last dose of study drug, OR 4. Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) 8. Screening clinical laboratory values as specified below: 1. Bone marrow reserve consistent with: absolute neutrophil count (ANC) ≥ 1.5 x 10\^9; platelet count ≥ 100 x 10\^9; hemoglobin ≥ 9 g/dL without transfusion within 1 week preceding study drug administration 2. Hepatic: total bilirubin ≤ 1.5 x upper limit of normal (ULN), transaminases (aspartate aminotransferase/serum glutamic oxaloacetic transaminase-AST/SGOT and alanine aminotransferase/serum glutamic pyruvic transaminase-ALT/SGPT) ≤ 2.5 x ULN (≤ 5 x ULN if liver metastases are present); 3. Renal: creatinine clearance ≥60 mL/min based either on cockroft-Gault estimate or based on urine collection (12 or 24 hour); 4. Metabolic: Glycosylated hemoglobin (HbA1c)\<7.0%, fasting serum glucose (≤ 130 mg/dL) and fasting triglycerides ≤ 300 mg/dL 9. Ability to swallow oral medications. 10. Must be able to fast for glucose monitoring throughout PIKTOR treatment. 11. Patients who have a history of brain metastasis are eligible for the study provided that all the following criteria are met: 1. Brain metastases which have been treated 2. No evidence of disease progression for ≥2 months before the first dose of study drug. 3. No hemorrhage after treatment 4. Off-treatment with dexamethasone for 3 weeks before administration of the first dose of PIKTOR 5. No ongoing requirement for dexamethasone or anti-epileptic drugs 12. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. Exclusion Criteria: Patients meeting any of the following exclusion criteria are not to be enrolled in the study: 1. Leptomeningeal disease that is symptomatic or cytology-proven. 2. Other clinically significant co-morbidities, such as uncontrolled pulmonary disease, active central nervous system disease, active infection, or any other condition that could compromise the patient's participation in the study. 3. Known human immunodeficiency virus infection. 4. Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection. 5. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. 6. Diagnosed or treated for another malignancy within 2 years before administration of the first dose of study drug, or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with non-melanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. 7. Breast feeding or pregnant. 8. Treatment with any investigational products within 30 days before the first dose of study drug 9. Previous treatment with PI3K, AKT, dual PI3K/mTOR inhibitors, TORC1/2 inhibitors or TORC1 inhibitors. 10. Manifestations of malabsorption due to prior gastrointestinal (GI) surgery, GI disease, or for an unknown reason that may alter the absorption of PIKTOR. In addition, patients with enteric stomata are also excluded. 11. History of any of the following within the last 6 months before administration of the first dose of the drug: 1. Ischemic myocardial event, including angina requiring therapy and artery revascularization procedures 2. Ischemic cerebrovascular event, including transient ischemic attack and artery revascularization procedures 3. Requirement for inotropic support (excluding digoxin) or serious (uncontrolled) cardiac arrhythmia (including atrial flutter/fibrillation, ventricular fibrillation or ventricular tachycardia) 4. Placement of a pacemaker for control of rhythm 5. New York Heart Association (NYHA) Class III or IV heart failure f. Pulmonary embolism 12. Significant active cardiovascular or pulmonary disease including: 1. Uncontrolled hypertension (ie, systolic blood pressure \>180 mm Hg, diastolic blood pressure \> 100 mm Hg). Use of anti-hypertensive agents to control hypertension before Cycle1 Day 1 is allowed. 2. Pulmonary hypertension 3. Need for supplemental oxygen 4. Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention, or history of valve replacement 5. Medically significant (symptomatic) bradycardia 6. History of arrhythmia requiring an implantable cardiac defibrillator 7. Baseline prolongation of the rate-corrected QT interval (QTc) (eg, repeated demonstration of QTc interval \> 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointes) 13. Poorly controlled diabetes mellitus defined as glycosylated hemoglobin (HbA1c) \> 7%; patients with a history of transient glucose intolerance due to corticosteroid administration may be enrolled in this study if all other inclusion/exclusion criteria are met. 14. Treatment with strong inhibitors and/or inducers of cytochrome P450 (CYP) 3A4, CYP2C19 or CYP2C19 within 1 week preceding the first dose of study drug (See Appendix IV). 15. Patients receiving systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug. 16. Daily or chronic use of a proton pump inhibitor (PPI) and/or having taken a PPI within 7 days before receiving the first dose of study drug