Inclusion Criteria

        Each patient must meet all of the following inclusion criteria to be enrolled in the study:

        Phase 1b and Phase 2

          1. Advanced or metastatic breast cancer.

          2. Histological or cytological confirmation of ER+ status (defined as > 1% positive tumor
             cells), and histological or cytological confirmation of HER2-negative (HER2-) status
             by local laboratory testing using criteria in the American Society of Oncology
             (ASCO)/College of American Pathologists (CAP) Clinical Practice Guideline update.

          3. Female patients 18 years of age or older who are postmenopausal for at least 1 year
             before the Screening visit, where menopause is defined by: Age ≥ 55 years and 1 year
             or more of amenorrhea. Surgical menopause with bilateral oophorectomy

             Age < 55 years and 1 year or more of amenorrhea, with an estradiol assay < 20 pg/mL

             Note: Ovarian radiation or treatment with a luteinizing hormone-releasing hormone
             agonist (goserelin acetate or leuprolide acetate) is not permitted for induction of
             ovarian suppression.

          4. Have a history of brain metastasis are eligible for the study provided that all the
             following criteria are met:

             Brain metastases which have been treated

               -  No evidence of disease progression for ≥ 3 months or hemorrhage after treatment

               -  Off-treatment with dexamethasone for 4 weeks before administration of the first
                  dose of MLN0128

               -  No ongoing requirement for dexamethasone or anti-epileptic drugs

          5. Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2.

          6. Clinical laboratory values as specified below within 4 weeks before the first dose of
             MLN0128:

               -  Bone marrow reserve consistent with absolute neutrophil count (ANC) ≥ 1.5 x
                  10^9/L; platelet count ≥ 100 x 10^9/L; hemoglobin ≥ 9 g/dL

               -  Total bilirubin ≤ 1.5 x the upper limit of the normal range (ULN), aspartate
                  aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN (≤ 5 x ULN
                  if liver metastases are present)

               -  Creatinine clearance ≥ 50 mL/min based either on Cockcroft-Gault estimate or
                  based on a 12- or 24-hour urine collection

               -  Fasting serum glucose ≤ 130 mg/dL and fasting triglycerides ≤ 300 mg/dL

          7. Left ventricular ejection fraction (LVEF) within 5 absolute percentage points of
             institutional standard of normal as measured by echocardiogram (ECHO) or multiple
             gated acquisition scan (MUGA) within 4 weeks before the first dose of MLN0128 (ie, if
             the institutional standard of normal is 50%, LVEF may be as low as 45% to be eligible
             for the study).

          8. Able to provide paraffin blocks or a minimum of 10 unstained slides of available
             archival tumor tissues (paraffin blocks are preferred). If archival tumor tissue is
             not available, a tumor biopsy may be performed before the patient begins treatment
             with MLN0128. If fewer than 10 slides are available or the tumor content/area
             requirements are not met, study eligibility will be determined upon discussion with
             the sponsor.

          9. Ability to swallow oral medications, willingness to perform mucositis prophylaxis, and
             suitable venous access for the study-required blood sampling.

         10. Voluntary written consent must be given before the 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.

             Phase 1b Only: In addition to the previously mentioned inclusion criteria, each
             patient must meet the following inclusion criterion to be enrolled in the phase 1b
             portion of the study:

         11. Patients may have SD or disease progression during their most recent treatment with
             exemestane or fulvestrant, or everolimus in combination with either exemestane (any
             country) or fulvestrant (US only). Exemestane or fulvestrant in combination with
             MLN0128 can also be initiated as a new line of therapy.

             Phase 2 Only: In addition to the previously mentioned inclusion criteria, each patient
             must meet all of the following inclusion criteria to be enrolled in the phase 2
             portion of the study:

         12. Measurable disease defined as follows:

               -  At least 1 extra-osseous lesion that can be accurately measured in at least 1
                  dimension. The lesion must measure ≥ 20 mm with conventional imaging techniques
                  or ≥ 10 mm with spiral computed tomography (CT) or magnetic resonance imaging
                  (MRI), or

               -  Bone lesions (lytic or mixed [lytic plus sclerotic]) in the absence of measurable
                  disease as defined above

         13. Patients must have had disease progression during treatment with everolimus in
             combination with either exemestane (any country) or fulvestrant (US only) (duration of
             treatment ≥ 4 weeks) and must have tolerated everolimus treatment in combination with
             exemestane (any country) or fulvestrant (US only) adequately according to the treating
             physician's judgment. Everolimus in combination with exemestane or fulvestrant is not
             required to be the most recent treatment before enrollment, but progression on the
             most recent anticancer therapy is required for enrollment.

        Exclusion Criteria

        Patients meeting any of the following exclusion criteria are not to be enrolled in the
        study:

        Phase 1b and Phase 2

          1. Prior anticancer therapy or other investigational therapy within 2 weeks before
             administration of the first dose of MLN0128 (except for exemestane or fulvestrant,
             which should be continued). Treatment with everolimus must be discontinued 2 weeks
             before administration of the first dose of MLN0128.

          2. Chronic concomitant therapy with bisphosphonates or denosumab for the prevention of
             bone metastases. Concomitant treatment with bisphosphonates or denosumab is permitted
             for treatment of osteoporosis or management of existing bone metastases if initiated
             at least 4 weeks before administration of the first dose of MLN0128.

          3. Initiation of treatment with hematopoietic growth factors, transfusions of blood and
             blood products, or systemic corticosteroids (either IV or oral steroids, excluding
             inhalers) within 1 week before administration of the first dose of MLN0128 (patients
             already receiving erythropoietin on a chronic basis for ≥ 4 weeks are eligible).

          4. Previous treatment with dual PI3K/mTOR inhibitors or TORC1/2 inhibitors.

          5. Manifestations of malabsorption due to prior gastrointestinal (GI) surgery, GI
             disease, or for an unknown reason that may alter the absorption of MLN0128.

          6. 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.

          7. Other clinically significant co-morbidities, such as uncontrolled pulmonary disease,
             active central nervous system disease, active infection, or any other condition that
             could compromise participation of the patient in the study.

          8. Known human immunodeficiency virus infection.

          9. History of any of the following within the last 6 months before administration of the
             first dose of MLN0128:

               -  Ischemic myocardial event, including angina requiring therapy and artery
                  revascularization procedures

               -  Ischemic cerebrovascular event, including transient ischemic attack and artery
                  revascularization procedures

               -  Requirement for inotropic support (excluding digoxin) or serious (uncontrolled)
                  cardiac arrhythmia (including atrial flutter/fibrillation, ventricular
                  fibrillation, or ventricular tachycardia)

               -  Placement of a pacemaker for control of rhythm

               -  New York Heart Association Class III or IV heart failure

               -  Pulmonary embolism

         10. Significant active cardiovascular or pulmonary disease before administration of the
             first dose of MLN0128, including:

               -  Uncontrolled hypertension (ie, systolic blood pressure > 180 mm Hg; diastolic
                  blood pressure > 95 mm Hg)

               -  Pulmonary hypertension

               -  Uncontrolled asthma or oxygen saturation < 90% by arterial blood gas analysis or
                  pulse oximetry on room air

               -  Significant valvular disease; severe regurgitation or stenosis by imaging
                  independent of symptom control with medical intervention; or history of valve
                  replacement

               -  Medically significant (symptomatic) bradycardia

               -  History of arrhythmia requiring an implantable cardiac defibrillator

               -  Baseline prolongation of the rate-corrected QT interval (QTc; eg, repeated
                  demonstration of QTc interval > 480 ms, or history of congenital long QT
                  syndrome, or torsades de pointes)

         11. Diagnosed or treated for another malignancy within 2 years before administration of
             the first dose of MLN0128 or previously diagnosed with another malignancy and have any
             evidence of residual disease. Patients with nonmelanoma skin cancer or carcinoma in
             situ of any type are not excluded if they have undergone complete resection.

             Phase 1b Only: In addition to the previously mentioned exclusion criteria, patients
             meeting the following exclusion criterion are not to be enrolled in the phase 1b
             portion of the study:

         12. More than 3 prior chemotherapy regimens for locally advanced or metastatic disease.

             Phase 2 Only: In addition to the previously mentioned exclusion criteria, patients
             meeting the following exclusion criterion are not to be enrolled in the phase 2
             portion of the study:

         13. More than 1 prior chemotherapy regimen for locally advanced or metastatic disease.