Inclusion Criteria:

          -  Patients must have histologically-confirmed HER2-positive breast cancer that is
             locally advanced or metastatic (stage 4); ideally this should be from biopsy of the
             metastatic disease; however if this is not available, histologic confirmation from the
             primary tumor is acceptable

          -  Patients must have had progression on a trastuzumab and taxane-based chemotherapy
             regimen during or after treatment for locally advanced or metastatic disease or within
             6 months after treatment for early-stage HER2-positive disease documented by one of
             the following results using Food and Drug Administration (FDA)-approved testing
             methods:

               -  Fluorescence in situ hybridization (FISH)-positive (with an amplification ratio
                  >= 2.0 indicating positive status) and/or

               -  Immunohistochemistry (IHC) 3 + by local laboratory assessment

          -  Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status =<
             2

          -  Patients must have a life expectancy >= 90 days

          -  Patients must have baseline laboratory tests within the following parameters at least
             4 weeks (28 days) prior to registration:

               -  Hemoglobin > 8 g/dL (which may be reached by transfusion)

               -  Platelet count >= 100 x 10^9/L (no transfusion allowed within 2 weeks)

               -  Absolute neutrophil count (ANC) >= 1.5 x 10^9/L without growth factor support

               -  Serum bilirubin =< 1.5 x upper limit of normal (ULN)

               -  Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT)
                  and/or alanine aminotransferase (ALT)/serum glutamate pyruvate transaminase
                  (SGPT) =< 2.5 x upper limit of normal (ULN) or =< 5 x ULN if liver metastases are
                  present

               -  Serum creatinine =< 1.5 x ULN or calculated or directly measured creatinine
                  clearance (CrCl) >= 50% LLN (lower limit of normal)

               -  Fasting plasma glucose (FPG) < 140 mg/dL/7.8 mmol/L

          -  Patients with child-bearing potential must have a negative urine pregnancy test within
             7 days prior to registration

          -  Patients must have a baseline electrocardiogram (ECG) showing QT interval =< 460 msec
             within 14 days prior to registration

          -  Patients must provide written informed consent prior to any registration on study

          -  Patients must be willing and able to comply with scheduled visits, treatment plan and
             laboratory tests

          -  Patient must be able to swallow and retain oral medication

        Exclusion Criteria:

          -  Patients with prior sensitivity or intolerance to PI3K inhibitors are not eligible for
             participation

          -  Patients with a history of grade >= 3 hypersensitivity reaction to trastuzumab, OR
             grade >= 1 with the most recent trastuzumab infusion before study entry, OR continued
             requirement for prolonged trastuzumab infusions to prevent hypersensitivity reactions
             are not eligible for participation

          -  Patients with a history of intolerance to trastuzumab and/or adverse events related to
             trastuzumab that resulted in trastuzumab being permanently discontinued are not
             eligible for participation

          -  Patients who have received prior treatment with T-DM1 are not eligible for
             participation

          -  Patients who have received prior anti-cancer therapy (e.g., biologic or other targeted
             therapy, chemotherapy, hormonal therapy) within 2 weeks prior to registration are not
             eligible for participation

          -  Patients with central nervous system (CNS) involvement may participate if the patient
             meets all of the following criteria:

               -  At least 4 weeks from prior therapy completion (including radiation and/or
                  surgery) to starting the study treatment

               -  Clinically stable with respect to the CNS tumor at the time of screening

               -  Not receiving steroid therapy

               -  Not receiving enzyme inducing anti-epileptic medications that were started for
                  brain metastases

          -  Patients who have received radiotherapy =< 4 weeks prior to registration, with the
             exception of palliative radiotherapy, who have not recovered from side effects of such
             therapy to baseline or grade =< 1 and/or from whom >= 30% of the bone marrow was
             irradiated are not eligible for participation

          -  Patients who have undergone major surgery =< 4 weeks prior to registration or who have
             not recovered from side effects of such procedure are not eligible for participation

          -  Patients with clinically significant cardiac disease or impaired cardiac function are
             not eligible for participation; this includes patients with:

               -  Congestive heart failure (CHF) requiring treatment (New York Heart Association
                  [NYHA] grade >= 2)

               -  Left ventricular ejection fraction (LVEF) < 50% as determined by multi-gated
                  acquisition (MUGA) scan or echocardiogram (ECHO)

               -  Uncontrolled arterial hypertension defined by blood pressure > 140/100 mm Hg at
                  rest (average of 3 consecutive readings)

               -  History or current evidence of unstable, clinically significant cardiac
                  arrhythmias or patients that require medications with a narrow therapeutic
                  window, atrial fibrillation and/or conduction abnormality (e.g. congenital long
                  QT syndrome, high-grade/complete atrioventricular [AV]-blockage)

               -  Acute coronary syndromes (including myocardial infarction, unstable angina,
                  coronary artery bypass graft [CABG], coronary angioplasty, or stenting), < 3
                  months prior to screening

               -  QT interval adjusted according to Fridericia (QTcF) > 460 msec on screening ECG

          -  Patients with diabetes mellitus requiring insulin treatment and/or with clinical signs
             or with fasting plasma glucose (FPG) >= 140 mg/dL/7.8 mmol/L, or history of documented
             steroid-induced diabetes mellitus are not eligible for participation

          -  Patients exhibiting any other condition that would, in the Investigator's judgment,
             preclude patient's participation in the clinical study due to safety concerns or
             compliance with clinical study procedures are not eligible for participation; this
             might include, but is not limited to, infection/inflammation, intestinal obstruction,
             and/or social/psychological complications

          -  Patients with impaired gastrointestinal (GI) function or GI disease that may
             significantly alter the absorption of oral BYL719 (e.g. ulcerative disease,
             uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel
             resection) are not eligible for participation

          -  Patients who are currently receiving medication with a known risk of prolonging the QT
             interval or inducing Torsades de Pointes (TdP) AND are unable to discontinue this
             medication or switch to a different medication prior to beginning study treatment are
             not eligible for participation

          -  Patients with a history of another malignancy within 2 years prior to registration are
             not eligible for participation; NOTE: the exceptions to this include cured basal cell
             carcinoma of the skin or excised carcinoma in situ of the cervix

          -  Patients receiving therapeutic doses of warfarin are not eligible for participation;
             NOTE: Patients with a need for therapeutic anticoagulation should be given low
             molecular weight heparin or other non-warfarin product

          -  Pregnant or nursing (lactating) women are not eligible for participation; NOTE:
             Pregnancy is defined as the state of a female after conception and until the
             termination of gestation, confirmed by a positive human chorionic gonadotropin (hCG)
             laboratory test (> 5 mIU/mL)

          -  Women of child-bearing potential, defined as all women physiologically capable of
             becoming pregnant, are not eligible for participation UNLESS they agree to use highly
             effective methods of contraception during dosing and for 5 weeks after study drugs
             discontinuation; highly effective contraception methods include:

               -  Total abstinence (when this is in line with the preferred and usual lifestyle of
                  the subject); periodic abstinence (e.g. calendar, ovulation, symptothermal,
                  post-ovulation methods) and withdrawal are not acceptable methods of
                  contraception

               -  Female sterilization (have had surgical bilateral oophorectomy with or without
                  hysterectomy) or tubal ligation at least 5 weeks before receiving study
                  treatment. In case of oophorectomy alone, the reproductive status of the woman
                  must have been confirmed by follow up hormone level assessment

               -  Male sterilization (at least 6 months prior to screening); for female subjects on
                  the study the vasectomized male partner should be the sole partner for that
                  subject

               -  Combination of the following:

                    -  Placement of an intrauterine device (IUD) or intrauterine system (IUS)

                    -  Barrier methods of contraception: condom or occlusive cap (diaphragm or
                       cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal
                       suppository

                         -  NOTE: Oral contraceptives (OC), injected or implanted hormonal methods
                            are not allowed as the sole method of contraception, as BYL719 has not
                            been characterized with respect to its potential to interfere with the
                            PK and/or the effectiveness of OCs