Inclusion Criteria:

          1. Women (or men) with histologically confirmed metastatic breast cancer.

          2. Hormone receptor positive (HR+) and no Her2 over-expression, according to local
             assessment.

          3. Presence of PIK3CA mutation on exon 9 or 20, determined on metastatic tissue specimen
             (frozen or FFPE) or plasma (ctDNA). Eligible plasma should have been collected at time
             of metastatic disease progression and before to initiating chemotherapy.

          4. Patient's disease is resistant to endocrine therapy (defined either as a relapse or
             progression occurred during endocrine therapy, whatever the line, or less than 12
             months after the end of endocrine therapy in adjuvant context).

          5. Patients who received 6 to 8 cycles of a first line chemotherapy, or patients who
             received 6 to 8 cycles of a first line stopped for progression followed by 6 to 8
             cycles of a 2nd line chemotherapy, and who are presenting a stable or a responding
             disease at the time of randomization (4 full cycles of chemotherapy are accepted if
             stopped for toxicity reasons)

          6. Age ≥18 years

          7. WHO Performance Status 0/1

          8. Presence of measurable or evaluable disease according to RECIST criteria v1.1

          9. Patients will have had a wash-out period of at least 14 days for weekly (except
             monoclonal antibodies) or daily chemotherapies or 28 days for other chemotherapies
             from last chemotherapy administration prior to randomization and should have recovered
             from all residual toxicities (grade ≤1), excluding alopecia.

         10. Patient has adequate bone marrow and organ function as defined by the following
             laboratory values:

               1. Absolute Neutrophil Count (ANC) ≥1.5 x 10⁹/L

               2. Platelets ≥100 x 10⁹/L

               3. Hemoglobin ≥9.0 g/dL

               4. International normalized ratio (INR) ≤1.5

               5. Potassium, magnesium and calcium (corrected for albumin), within normal limits
                  for the institution, or ≤Grade 1 severity according to NCI-CTCAE version 4.03 if
                  judged clinically not significant by the investigator

               6. Serum creatinine ≤1.5 x upper limit of normal (ULN) or creatinine clearance ≥50
                  mL/min (Measured or calculated by Cockcroft and Gault formula)

               7. Total serum bilirubin ≤ ULN (or ≤1.5 x ULN if liver metastases are present; or
                  total bilirubin ≤3.0 x ULN with direct bilirubin within normal range in patients
                  with well documented Gilbert's Syndrome)

               8. Alanine aminotransferase (AST) and aspartate aminotransferase (ALT) ≤2.5 ULN (or
                  <5.0 x ULN if liver metastases are present)

               9. Fasting plasma glucose (FPG) ≤140 mg/dL or ≤7.7 mmol/L* and Glycosylated
                  Hemoglobin (HbA1c) ≤6.4% (both criteria have to be met).

                    -  For patients with FPG ≥100 mg/dL or HbA1c ≥5.7% (i.e. threshold for
                       pre-diabetes) at baseline, recommend lifestyle changes according to ADA
                       guidelines, i.e. dietary advice (e.g. small frequent meals, low carbohydrate
                       content, high fiber, balancing carbohydrate intake over the course of the
                       day, three small meals and 2 small snacks rather than one large meal) and
                       exercise. A consultation with a diabetologist is highly recommended

         11. Provision of signed and dated, written informed consent prior to any study specific
             procedures, sampling and analysis

         12. Patient with social insurance coverage.

        Exclusion Criteria:

          1. Spinal cord compression or symptomatic or progressive brain metastases (unless
             asymptomatic or treated and stable without steroids during the last 30 days).

          2. Patient has received more than 2 previous lines of chemotherapy for metastatic disease
             before randomization.

          3. Prior exposure to anthracyclines or mitoxantrone with cumulative exposure in excess of
             360 mg/m² for doxorubicin, 720 mg/m² for epirubicin, or 72 mg/m² for mitoxantrone.

          4. In the Investigator's judgment, patient has a life expectancy <3 months .

          5. Disease progression occuring before randomization.

          6. Patient has received prior treatment with any PI3K or AKT inhibitor (mTOR inhibitors
             are allowed)

          7. Patient has history of hypersensitivity to any drugs or metabolites of similar
             chemical classes as alpelisib, or history of hypersensitivity to active or inactive
             excipients of any other study treatment.

          8. Patient has not recovered to grade 1 or better (except alopecia) from related side
             effects of any prior antineoplastic therapy

          9. Patient has received radiotherapy ≤4 weeks or limited field radiation for palliation
             ≤2 weeks prior to randomization, and who has not recovered to grade 1 or better from
             related side effects of such therapy (with the exception of alopecia) or from whom
             ≥25% of the bone marrow was irradiated

         10. Patient has participated to another clinical study with an investigational product
             during the last 30 days.

         11. Patient has had major surgery within 14 days prior to starting study treatment or has
             not recovered from major side effects

         12. Patient is currently receiving or has received systemic corticosteroids ≤2 weeks prior
             to starting study treatment, or has not fully recovered from side effects of such
             treatment

         13. Patients with an established diagnosis of diabetes mellitus type I or not controlled
             type II, or documented steroid induced diabetes mellitus

         14. Patient who necessitates to maintain the following drugs during study treatment :

               -  Drugs known to be strong inhibitors or inducers of isoenzyme CYP3A4 including
                  herbal medications (list of prohibited CYP3A4 inhibitors and inducers provided in
                  Table 12)

               -  Drugs with a known risk to induce Torsades de Pointes (list of prohibited QT
                  prolonging drugs provided in Table 12) Note: The patient must have discontinued
                  strong inducers for at least one week and must have discontinued strong
                  inhibitors before the study treatment is initiated. Switching to a different
                  medication prior to starting study treatment is allowed.

         15. Patient is currently receiving warfarin or other coumarin derived anti-coagulant for
             treatment, prophylaxis or otherwise. Therapy with heparin, low molecular weight
             heparin (LMWH), or fondaparinux is allowed.

         16. Patients who have other concurrent severe or uncontrolled medical conditions that
             would, in the Investigator's judgment, contraindicate patient participation in the
             individual patient program (eg. active or uncontrolled severe infection, chronic
             active hepatitis, immuno-compromised, acute or chronic pancreatitis, uncontrolled high
             blood pressure, interstitial lung disease, etc.)

         17. Patient has currently documented pneumonitis

         18. Patient has a known history of HIV infection (testing not mandatory)

         19. Patient 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 (LVEF) <50% as determined by Multiple Gated
                  acquisition (MUGA) scan or echocardiogram (ECHO)

               -  myocardial infarction ≤6 months prior to enrolment

               -  unstable angina pectoris

               -  serious uncontrolled cardiac arrhythmia

               -  symptomatic pericarditis

               -  QTcF >480 msec on the baseline ECG (using the QTcF formula) currently receiving
                  treatment with medication that has a known risk to prolong the QT interval or
                  inducing Torsades de Pointes, and the treatment cannot be discontinued or
                  switched to a different medication prior to starting study treatment (list of
                  prohibited QT prolonging drugs provided in Table 12)

         20. Patient has impairment of gastrointestinal (GI) function or GI disease that may
             significantly alter the absorption of any study treatment (e.g., ulcerative diseases,
             uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel
             resection)

         21. Patient had previous or current malignancies of other histologies within the last 5
             years, with the exception of in situ carcinoma of the cervix, and adequately treated
             basal cell or squamous cell carcinoma of the skin.

         22. Pregnant or nursing (lactating) women.

         23. Patient who does not accept to comply with highly effective contraception methods
             during the study treatment and through the duration as defined below after the final
             dose of study treatment:

               -  Sexually active males should use a condom during intercourse while taking drug
                  and for at least 4 weeks after the final dose of study treatment and should not
                  father a child in this period.

               -  Women of child-bearing potential must use highly effective contraception during
                  study treatment and for at least 4 weeks after the final dose of study treatment
                  and until resumption of menses (if longer than 4 weeks).

         24. Patient has a history of non-compliance to medical regimen or inability to grant
             consent

         25. Individuals deprived of liberty or placed under the authority of a tutor