Inclusion Criteria:

          -  Patients with HER2/neu overexpressing metastatic breast, not considered curable by
             conventional therapies

               -  HER2 positivity will be defined per the 2018 American Society of Clinical
                  Oncology/College of American Pathologists (ASCO/CAP) guidelines (Journal of
                  Clinical Oncology [JCO] 2018)

               -  Extra-skeletal disease that can be accurately measured >= 10 mm by standard
                  imaging techniques within 28 days of treatment

          -  Patients must continue trastuzumab with or without pertuzumab dosing per standard of
             care through the entire study period

          -  Prior lapatinib in the metastatic setting is allowed, but not required

          -  Patients with estrogen receptor (ER) and / or progesterone receptor (PR) positive
             metastatic breast cancer are eligible and may continue anti-estrogen therapy for the
             duration of the study

          -  Patients must be at least 14 days post cytotoxic chemotherapy prior to enrollment

          -  Patients must be at least 14 days post immunosuppressant prior to enrollment

          -  Patients on bisphosphonates and/or endocrine therapy are eligible and can continue on
             this therapy concurrently

          -  Women who are having sex that can lead to pregnancy must have a negative pregnancy
             test and must avoid becoming pregnant while on alpha-TEA and for 4 weeks after the
             last dose of alpha-TEA. Men must avoid fathering a child while on alpha-TEA and for 4
             weeks after the last dose of alpha-TEA

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

          -  Patients must have recovered from major infections and/or surgical procedures, and in
             the opinion of the investigator, not have significant active concurrent medical
             illnesses precluding study treatment

          -  White blood cell (WBC) >= 2000/mm^3 (within 28 days prior to first treatment)

          -  Hemoglobin (Hgb) >= 8 mg/dl (within 28 days prior to first treatment)

          -  Estimated creatinine clearance (Crcl) by the Cockcroft-Gault (C-G) equation >= 60
             mL/min (within 28 days prior to first treatment)

          -  Total bilirubin =< 1.5 x upper limit of normal (within 28 days prior to first
             treatment)

          -  Aspartate aminotransferase (AST) < 1.5 X upper limit of laboratory normal (within 28
             days prior to first treatment)

          -  Alanine aminotransferase (ALT) < 1.5 X upper limit of laboratory normal (within 28
             days prior to first treatment)

          -  Alkaline phosphatase < 2.5 X upper limit of laboratory normal (within 28 days prior to
             first treatment)

          -  International normalized ratio (INR) < 1.5 (within 28 days prior to first treatment)

          -  Prothrombin time (PT) < 16 seconds (within 28 days prior to first treatment)

          -  Partial thromboplastin time (PTT) < 38 seconds (within 28 days prior to first
             treatment)

          -  Ability to swallow capsules

          -  Patients must have adequate cardiac function as demonstrated by normal left
             ventricular ejection fraction (LVEF) >= the lower limit of normal for the facility on
             multi-gated acquisition (MUGA) scan or echocardiogram (ECHO) within 3 months of
             enrollment

          -  Must be off vitamin E supplements for at least two weeks prior to first dose of study
             drug

        Exclusion Criteria:

          -  Patients with any of the following cardiac conditions:

               -  Restrictive cardiomyopathy

               -  Unstable angina within 6 months prior to enrollment

               -  New York Heart Association functional class III-IV heart failure

               -  Symptomatic pericardial effusion

               -  Right atrial enlargement on ECHO would not be allowed

          -  History of or active atrial fibrillation or supraventricular tachycardia

          -  History of documented cardiac arrhythmia

          -  Active cardiac ischemia. Patients with a history of ischemia ameliorated with stent
             placement or coronary artery bypass grafting and who have no evidence of ischemia by
             exercise or physiological stress testing are eligible

          -  Patients with any clinically significant autoimmune disease requiring active treatment

          -  Patients receiving any concurrent systemic immunosuppressants. Patients who require
             brief courses of steroids to manage allergic reaction to intravenous contrast used in
             radiographic studies are eligible

          -  Patients receiving strong inhibitors or inducers of CYP3A4/5

          -  Patients who are pregnant or breast-feeding

          -  Patients who are simultaneously enrolled in other treatment studies

          -  Active brain metastatic disease. Patients with brain metastases who have been treated
             with surgery, gamma-knife radiosurgery or radiation and no radiographic progression
             for at least 4 weeks and off steroids are eligible

          -  Any medical or psychiatric condition that in the opinion of the principal investigator
             (PI) would preclude compliance with study procedures

          -  Malabsorption state such as ulcerative colitis, previous surgical resection of > 20%
             of intestine or stomach

          -  Surgery or severe trauma within 4 weeks of study entry (minimally invasive procedures
             acceptable)

          -  Corrected QT interval (QTc) greater than 450 msec at (calculated using Bazett's
             formula), sick-sinus syndrome or other active cardiac disease

          -  Prior blood clot or need for ongoing anti-coagulation therapy

          -  Patient with abnormal thyroid function or who are euthyroid but on medication for
             thyroid disorders must be excluded