Inclusion Criteria:
1. Female, Aged \> 18;
2. HER2-positive breast cancer are defined as immunohistochemical (IHC) testing as +++, or IHC++ with FISH testing of positive;
3. Histologically or cytologically confirmed invasive breast carcinoma with locally recurrent or radiological evidence of metastatic disease.
4. Patients with HER2-positive metastatic breast cancer who have progressed disease after trastuzumab treatment include the following four types of patients (Note: The following patients are in a parallel relationship):
1. Patients with HER2-positive breast cancer who have progressed during adjuvant trastuzumab treatment after surgery; or
2. Patients with HER2-positive breast cancer who have relapsed or metastasized after receiving adjuvant trastuzumab therapy; or
3. HER2-positive recurrent or metastatic BC patients who have progressed after receiving at least 4 weeks of trastuzumab as first-line treatment ; or
4. HER2-positive metastatic BC patients who have never been treated have progressed after receiving at least 4 weeks of trastuzumab as first-line treatment.
5. Genetic testing shows that the PI3K/Akt/mTOR pathway related genes are mutated;
6. ECOG PS score ≤2, estimated survival time ≥6 months, and can be followed-up;
7. Patients with measurable disease as per RECIST 1.1 criteria;
8. Cardiopulmonary function is basically normal, LVEF≥50% within 4 weeks before starting treatment;
9. An adequate liver function with the following definition:
1. Total bilirubin ≤ 1.5 times the upper limit of normal value. Patients with known Gibert's disease can be included in the group if combined bilirubin ≤ 1.5 times the upper limit of normal value;
2. AST and ALT ≤2.5 times the upper limit of the normal value; if there is liver metastasis, ≤5 times the upper limit of the normal value (the normal value is the normal value specified by this clinical trial center);
10. Have sufficient baseline hematology parameters, defined as follows:
1. ANC≥1.5 x 10\^3 /μL;
2. Platelet count ≥100 x 10\^3/μL, if it is 75-100 x 10\^3/μL, it may be included in the group, as long as the doctors believe it can be included;
3. Hemoglobin ≥9 g/dL.
11. Coagulation Indicators: International normalized ratio (INR) and activated partial thromboplastin time (aPTT) ≤ 1.5 times the upper limit of normal, unless drugs known to change INR and aPTT are used;
12. No history of serious heart, kidney and other important organs and endocrine disease;
13. Female patients of childbearing age have a negative pregnancy test and voluntarily take effective and reliable contraceptive measures;
14. The patients voluntarily signed an informed consent form.
Exclusion Criteria:
Anyone who has one of the following conditions cannot be selected for this trial:
1. Participated in other clinical trials within 4 weeks;
2. Have used mTOR inhibitors in the past;
3. Previous use of Pyrotinib in first-line treatment stage; previous use of lapatinib is allowed;
4. Accompanied by immunosuppressant or chronic corticosteroid medication, or more than 25% bone marrow radiotherapy within 4 weeks;
5. Symptomatic CNS metastases or evidence of leptomeningeal disease;
6. Gastrointestinal dysfunction or gastrointestinal diseases (including active ulcers);
7. Hepatitis B or hepatitis C carriers, or other known chronic liver diseases; HIV positive;
8. Known hypersensitivity to any study medication
9. Women during pregnancy or lactation;
10. Left ventricular ejection fraction \<50%; clinical manifestations of patients with obvious arrhythmia, myocardial ischemia, severe atrioventricular block, cardiac insufficiency, and severe valvular disease;
11. Any malignancy within 5 years prior to randomization, with the exception of adequately treated in-situ carcinoma of the cervix uteri, basal or squamous cell carcinoma;
12. The researchers decide that any other medical, social or psychological conditions which are inappropriate to participate in this trial.
