Alpelisib (BYL719) in Combination With Continued Endocrine Therapy Following Progression on Endocrine Therapy in Hormone Receptor Positive, HER2 Negative, PIK3CA Mutant Metastatic Breast Cancer

Eligibility Criteria Individuals from populations who are underrepresented in clinical research (e.g., racial and ethnic minorities, women, individuals from rural/frontier communities, older individuals) will be enrolled with a goal of ensuring that all eligible patients are given the opportunity to participate in novel clinical trials and that research findings can be generalizable to the entire population. Inclusion Criteria * Written informed consent and HIPAA authorization for release of personal health information. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Age ≥ 18 years at the time of consent. * ECOG Performance Status of 0-2 within 28 days prior to registration. * Men and postmenopausal female patients. Premenopausal patients (age 18 or older) who have been rendered postmenopausal will also be included. Postmenopausal is defined as: * Age \>= 55 years and one year or more of amenorrhea. * Age \< 55 years and one year or more of amenorrhea, with estradiol \< 20 pg/ml * Age \< 55 years with prior hysterectomy but intact ovaries, with estradiol \< 20 pg/ml * Prior bilateral oophorectomy NOTE: Women who do not fit the criteria for being postmenopausal as above are deemed premenopausal. Premenopausal patients (age 18 or older) who can be rendered postmenopausal will also be eligible. Methods eligible for rending premenopausal patients postmenopausal include: * Ongoing treatment with luteinizing hormone-releasing hormone (LHRH) agonist, with treatment starting at least 4 weeks prior to randomization and with estradiol \< 20 pg/ml. LHRH agonist must be administered within 7 days of scheduled administration date during the length of the clinical trial. * Histologically confirmed metastatic or unresectable (not amenable to curative therapy) breast cancer. * Has confirmed hormone receptor positivity with ER \>=1% and/or PR \>=1%. Preferred receptor testing is obtained from a metastatic site, but can be from the primary breast or axilla biopsy as long as this is most recent biopsy. * Has confirmed HER2 negative breast cancer. HER2 negative or non-amplified is determined by the current ASCO-CAP criteria which are as follows: HER2 testing by IHC as 0 or 1+. Or negative by in situ hybridization (FISH/CISH/SISH) defined as Her2/CEP17 ratio \<2 and for single probe assessment a HER2 copy number \<6). Preferred receptor testing is obtained from a metastatic site, but can be from the primary breast or axilla biopsy as long as this is most recent biopsy. * PIK3CA mutation identified via local testing from tumor tissue or blood. * Has either measurable disease, i.e. at least one measurable lesion as per RECIST 1.1 criteria OR if no measurable disease is present, then at least one predominantly lytic bone lesion must be present, within 28 days prior to registration. Patients with no measurable disease and only one predominantly lytic bone lesion that has been previously irradiated are eligible if there is documented evidence of disease progression of the bone lesion after irradiation. * Has received at least one line of therapy with an endocrine therapy or endocrine therapy combination with other agents in the metastatic setting. * Must have received endocrine therapy (aromatase inhibitor or fulvestrant as single agent or in combination with other agents) as last line of therapy with progressive disease, as determined by treating physician. * No more than two prior lines of endocrine therapy or endocrine therapy combinations in the metastatic setting. Transition from one nonsteroidal aromatase inhibitor to a second nonsteroidal aromatase inhibitor due to tolerance will only count as one line of endocrine therapy. Combination therapy will be considered one line even if one of the agents is discontinued and the other continued. * Patient must have received treatment with a CDK4/6 inhibitor for breast cancer in the metastatic setting. CDK4/6 inhibitor discontinuation due to intolerance or reasons other than progression is allowed. * Demonstrate adequate organ function as defined in the protocol; all screening labs to be obtained within 28 days prior to registration. * Men who are not surgically or medically sterile must agree to use an acceptable method of contraception. Acceptable forms of contraception include castration, vasectomy, and condom/occlusive cap with spermicidal foam/gel/film/cream/suppository. Male patients with female sexual partners who are pregnant, possibly pregnant, or who could become pregnant during the study must agree to use condoms at least one month after the last dose of study drug. Total abstinence for the same study period is an acceptable alternative. * Premenopausal females must agree to use an acceptable method of contraception or to abstain from sexual intercourse for the duration of their participation in the study and for 3 months after discontinuation of therapy. Adequate forms of contraception include: total abstinence, surgery intended to prevent pregnancy (defined as hysterectomy, bilateral oophorectomy or bilateral tubal ligation), non-hormonal IUD, or condom/occlusive cap with spermicidal foam/gel/film/cream/suppository). * As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial. Exclusion Criteria * Patients with prior chemotherapy for metastatic or advanced disease. * Active infection requiring systemic therapy. * Patients with a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen are not eligible for this trial. * Uncontrolled, active CNS metastases causing clinical symptoms or metastases that require therapeutic intervention, including leptomeningeal disease. NOTE: Subjects who are symptomatic and have not undergone prior brain imaging must undergo a head computed tomography (CT) scan or brain magnetic resonance imaging (MRI) within 28 days prior to registration to exclude brain metastases. * Treatment with any investigational drug within 14 days prior to registration. * Radiotherapy to index lesion \<= 4 weeks or limited field radiation to index lesion for palliation \<= 2 weeks prior to randomization. * Established diagnosis of diabetes mellitus type I or persistent poorly controlled diabetes mellitus, with an uninterrupted hemoglobin A1c \> 8.0% for 1 year or greater despite standard care. For patients with newly diagnosed diabetes mellitus without 1 year of hemoglobin A1c values, available hemoglobin A1c values cannot all be \> 8.0%. * Symptomatic visceral disease or any disease burden that makes the patient ineligible for endocrine therapy per the investigator's best judgment. * As determined by the enrolling physician or protocol designee, impairment of gastrointestinal function or disease that may significantly alter the absorption of the study drugs. * Currently documented clinically active pneumonitis. Patients could have received prior treatment for pneumonitis but pneumonitis must have clinically resolved and treatments for pneumonitis (e.g. steroids) must be completed prior to randomization. * Active cardiac disease, defined as any of the following within 6 months prior to the start of study treatment: * History of angina pectoris, coronary artery bypass graft, symptomatic pericarditis, or myocardial infarction. * History of documented congestive heart failure (New York Heart Association functional classification III-IV). * History of any cardiac arrhythmias, (e.g., ventricular tachycardia), complete left bundle branch block, high grade AV block (e.g., bifascicular block, Mobitz type II and third degree AV block), supraventricular, nodal arrhythmias, or conduction abnormality. * Systolic blood pressure (SBP) \>180 mmHg and/or Diastolic Blood Pressure (DBP) ≥ 100 mm Hg at screening. Initiation or adjustment of antihypertensive medication(s) is allowed prior to screening. * History of acute pancreatitis within 1 year of screening or a past medical history of chronic pancreatitis. * Prior treatment with PI3K, mTOR or AKT inhibitor in the metastatic setting. * History of chronic steroid use (defined as daily steroid use \> 14 days) and requirement for continued chronic steroid use.