Inclusion Criteria:

          -  Breast tumor with suspected PI3K-pathway dependence (either by mutation or by known
             biologic rationale. PI3K dependence includes the presence of a PIK3CA-mutant hotspot
             mutation, PIK3CA copy number gain, mTOR hotspot mutation, or PTEN loss in the archival
             or fresh tumor tissue specimen identified in K-MASTER panel. All genetic findings must
             be reviewed by the study PI, prior to study entry.).

          -  Patient is an adult, female ≥ 19 years old at the time of informed consent.

          -  Patient has histologically and/or cytologically confirmed diagnosis of HER2-positive
             breast cancer. HER2-positive breast cancer as defined by an immunohistochemistry (IHC)
             score of 3+ or gene amplified by in situ hybridization (ISH) as defined by a ratio of
             ≥ 2.0 for the number of HER2 gene copies to the number of chromosome 17
             copies.Metastatic or unresectable disease documented on diagnostic imaging studies.

          -  Metastatic or unresectable disease documented on diagnostic imaging studies.

          -  Prior 2 or more HER-2 directed therapy including trastuzumab for metastatic disease is
             mandatory.

          -  Patient must have at least one measurable lesion according to Response valuation
             Criteria in Solid Tumors version 1.1 (RECIST v.1.1).

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1.

          -  Adequate bone marrow and organ function including: WBC ≥ 3500/mL; Platelets ≥
             100,000/uL; Hemoglobin >9.0 g/dL; Total bilirubin ≤ 1.5x ULN; AST and ALT < 2.5 x ULN;
             Alkaline phosphatase <2.5x ULN; Creatinine ≤ 1.5x ULN or CCr >60 ml/min for patients
             with abnormal serum Cr level function.

          -  Adequate glucose control, as defined by HbA1c < 7% and fasting blood glucose ≤ 126
             mg/dL (7.0 mmoL/L).

          -  Adequate glucose control, as defined by HbA1c < 7% and fasting blood glucose ≤ 126
             mg/dL (7.0 mmoL/L).

          -  Life expectancy higher than 3 months

          -  Patient has an adequate left ventricular ejection function of at least 50 % at
             baseline, as measured by echocardiography.

          -  Written informed consent

        Exclusion Criteria:

          -  Patient is pregnant or lactating, where 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.

          -  Patient has received previous treatment with a mechanistic target of rapamycin (mTOR)
             inhibitor or phosphoinositide 3-kinase (PI3K) inhibitor.

          -  Patient has symptomatic and unstable CNS metastases, except for treated brain
             metastases. Treated brain metastases are defined as having no evidence of progression
             or hemorrhage after treatment and no ongoing requirement for dexamethasone, as
             ascertained by clinical examination and brain imaging (MRI or CT) during the screening
             period. Anticonvulsants (stable dose) are allowed.

          -  Active and clinically significant bacterial, fungal or viral infection including
             hepatitis B (HBV), hepatitis C (HCV), known human immunodeficiency virus syndrome
             (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness. Baseline viral
             assessment is not required in patients with no known infection.

          -  Current use or anticipated need for food or medications that are known moderate or
             greater CYP3A4 inhibitors, including their administration within 7-days prior to the
             first gedatolisib dose and while receiving investigational product (ie, strong CYP3A4
             inhibitors: grapefruit juice or grapefruit/grapefruit related citrus fruits [e.g.,
             Seville oranges, pomelos], ketoconazole, miconazole, itraconazole, voriconazole,
             posaconazole, clarithromycin, telithromycin, indinavir, saquinavir, ritonavir,
             nelfinavir, amprenavir, fosamprenavir nefazodone, lopinavir, troleandomycin,
             mibefradil, conivaptan; moderate CYP3A4 inhibitors: erythromycin, verapamil,
             atazanavir, delavirdine, fluconazole, darunavir, diltiazem, aprepitant, imatinib,
             tofisopam, ciprofloxacin, and cimetidine).

          -  Concurrent use or anticipated need for medications that are mainly metabolized by
             UGT1A9 including their administration within 7-days prior to the first dose of
             investigational product (e.g., propofol, propranolol, dapagliflozin, darexaban,
             mycophenolic acid, and tapentadol).

          -  Acetaminophen use within 24 hours before or after the first dose of gedatolisib.

          -  Current use or anticipated need for food or medications that are metabolized by
             CYP2D6, and of narrow therapeutic index including their administration within 10-days
             prior to the first gedatolisib dose and while receiving investigational product.

          -  Concurrent use of herbal preparations.

          -  Major surgery within 4 weeks of first dose of investigational product or not fully
             recovered from any side effects of previous procedures.

          -  Any other malignancy within 3 years prior to first dose of investigational product
             except for adequately treated basal cell or squamous cell skin cancer, or carcinoma in
             situ of the cervix.

          -  QTc interval >480 msec (based on the mean value of the triplicate ECGs), family or
             personal history of long or short QT syndrome, Brugada syndrome or known history of
             QTc prolongation or Torsade de Pointes.

          -  Any of the following within 6 months of first dose of investigational product
             myocardial infarction, severe/unstable angina, ongoing cardiac dysrhythmias of NCI
             CTCAE v. 5.0 Grade ≤2, atrial fibrillation of any grade, coronary/peripheral artery
             bypass graft, symptomatic congestive heart failure, cerebrovascular accident including
             transient ischemic attack, or symptomatic pulmonary embolism.

          -  History of interstitial pneumonitis.

          -  Other severe acute or chronic medical or psychiatric condition, including recent
             (within the past year) or active suicidal ideation or behavior, or laboratory
             abnormality that may increase the risk associated with study participation or
             investigational product administration or may interfere with the interpretation of
             study results and, in the judgment of the investigator, would make the patient
             inappropriate for entry into this study.