Phase II Trial of Alpelisib With iNOS Inhibitor and Nab-paclitaxel in Patients With HER2 Negative Metastatic or Locally Advanced Metaplastic Breast Cancer (MpBC)

Inclusion Criteria: 1. The patient (or legally acceptable representative if applicable) provides written informed consent for the study. 2. At least 18 years of age on the day of informed consent signing. 3. Histologically confirmed HER2 negative MpBC and/or Triple Negative Breast Cancer (TNBC) with squamous and/or sarcomatoid elements, including osseous, chondroid, and spindle morphology. 4. HER2 negative status as defined by the current American Society of Clinical Oncology and College of American Pathologists guidelines at time of study entry. 5. Locally advanced inoperable or metastatic MpBC with measurable disease by RECIST 1.1 Both first- and second-line patients will be eligible for this trial. Patients may have received prior immunotherapy, per standard of care. 6. Eastern Cooperative Oncology Group performance status of 0 or 1. 7. Adequate organ and marrow function as defined below: * Hemoglobin ≥9.0 g/dl (without blood transfusion within 2 weeks of laboratory test used to determine eligibility) * Absolute neutrophil count ≥1000/μL (without granulocyte colony stimulating factor support within 2 weeks of laboratory test used to determine eligibility) * Platelet count ≥100,000/μL (without transfusion within 2 weeks of laboratory test used to determine eligibility) * Serum total bilirubin (TB) ≤1.5 x institutional upper limit of normal (ULN; In the case of known Gilbert's syndrome, a higher serum TB \[\>1.5 x ULN\] is allowed), * Aspartate transaminase/alanine transaminase ≤5 x institutional ULN * Creatinine ≤1.5X the ULN or measured creatinine clearance ≥ 60 mL/min/1. 8. Fasting blood glucose of ≤140 mg/dl and HgbA1c ≤7.0. 9. Ability to swallow oral medication. 10. Ability to take aspirin. 11. Women of childbearing potential must agree to use contraception for the duration of the study through 90 days after the last dose of study treatment. A condom is required for all sexually active male participants to prevent them from fathering a child AND to prevent delivery of study treatment via seminal fluid to their partner. In addition, male participants must not donate sperm during the study and up to the time period as specified in labels of study drugs. 12. If patient received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting the study treatment. 13. Willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations. Exclusion Criteria: 1. Concomitant use of strong inhibitors or strong inducers of cytochrome P450 (CYP)3A4. The patient must have discontinued strong CYP3A4 inhibitors or strong CYP3A4 inducers for at least 1 week prior to study treatment initiation (Examples included in Appendix 2). 2. Currently receiving warfarin or other coumarin-derived anticoagulant for treatment, prophylaxis, or otherwise. Therapy with DOACs, heparin, low molecular weight heparin, direct oral anticoagulants or fondaparinux is allowed. 3. Concurrent use of medications that interact with nitrate/nitrite levels (Examples included in Appendix 3). 4. Received previous treatment with nab-paclitaxel, Pl3K inhibitor, AKT inhibitor, or mTOR inhibitor. 5. Known history of Steven Johnson's syndrome or toxic epidermal necrolysis. 6. Since HAART agents are metabolized by CYP3A4, HIV positive patients will be excluded from this trial. 7. Poorly controlled hypertension at baseline (defined as systolic blood pressure \>150 mm Hg). Isolated, unconfirmed systolic BP elevations will NOT exclude participation. Patients with medication-controlled hypertension are allowed provided they have been on their current medications for at least 4 weeks prior to Cycle 1, Day 1. 8. Has any of the following cardiac abnormalities: * Symptomatic congestive heart failure * History of documented congestive heart failure (New York Heart Association functional classification III-IV) * Documented cardiomyopathy * Left ventricular ejection fraction \<50% as determined by multigated acquisition scan or echocardiogram * Myocardial infarction \~6 months prior to enrollment * Unstable angina pectoris * Serious uncontrolled cardiac arrhythmia * Symptomatic pericarditis * History of congenital QT prolongation * Absolute corrected QT interval of \>480 msec in the presence of potassium \>4.0 mEq/L and magnesium \>1.8 mg/dl. 9. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 3 weeks prior to study treatment administration. NOTE: Patients who have entered the follow-up phase of an investigational study may participate as long as it has been 3 weeks after the last dose of the previous investigational agent. 10. Known or suspected hypersensitivity to any component or excipient of the proposed regimen (nab-paclitaxel, alpelisib, iNOS inhibitor, aspirin). 11. Known additional malignancy that requires active treatment. 12. Pneumonitis/ interstitial lung disease on baseline CT scan of the chest or moderate to severe chronic lung disease 13. Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study. 14. Manifestations of malabsorption due to prior gastrointestinal surgery, gastrointestinal surgery disease, or an unknown reason. 15. Symptomatic/untreated metastatic central nervous system disease. 16. Type I diabetes mellitus irrespective of Hgb A1c OR uncontrolled type II diabetes mellitus defined as hemoglobin A1c \>7%. 17. Uncontrolled gastric ulcer 18. ≥ Grade 2 sensory neuropathy 19. Osteonecrosis of jaw 20. Pancreatitis 21. Pregnant, breastfeeding or expecting to conceive children within the projected duration of the study, starting with the prescreening or screening visit through 30 days after the last dose of study treatment.