This study is being done for the following reasons:

The study has two parts. The purpose of the first part (Phase I) of the study is to find out the highest dose of Afatinib that can be given safely with T-DM1.

The purpose of the second part of the study (Phase II) is to find out whether the dose of Afatinib with T-DM1 determined in Phase I will keep breast cancer from getting worse for a period of time.

This is a prospective, randomized, 2-arm, multicenter study to compare the safety and efficiency of T-DM1 + Afatinib versus T-DM1 in HER2-positive breast cancer patients with active refractory brain metastases. This study will be divided into two phases. The purpose of Phase I is to find out the highest dose of Afatinib that can be given safely with T-DM1. 3 ~ 24 eligible subjects will be enrolled in the study. The purpose of Phase II is to find out whether the dose of Afatinib with T-DM1 determined in Phase I will keep subjects from getting worse for a period of time. The estimated ORR is 17.9 percent in the control group, hypothesis Afatinib can improve the prognosis of subjects, so objective respond rate (ORR) of experimental group is increased by 30 percent, with alpha = 0.025 (unilateral), beta = 0.1. The ratio of the experimental group and control group is 1:1, assuming a 5 percent loss rate. As a result, calculating by PASS 11 software, approximately 106 subjects will be enrolled, with 53 cases in the experimental group, and 53 cases in the control group.

Inclusion Criteria:

• Patients provided written informed consent
• Women aged 18-75 years old
• Histologically or cytologically confirmed HER2-positive (IHC 3+ or ISH+) breast cancer
• Patients with HER2 positive breast cancer with a documented central nervous system (CNS) recurrence/progression (by imaging) during or after a HER2 inhibitor (Trastuzumab and/or Lapatinib, Pyrotinib, Tucatinib) based therapy
• At least one measurable and progressive lesion in the CNS (≥10 mm on T1-weighted, gadolinium-enhanced MRI)
• Previous treatment with HER2 inhibitors to be discontinued prior to first study treatment administration (at least 14 days for trastuzumab and other antibodies, at least 7 days for lapatinib)
• Previous chemotherapy and hormonal therapy (adjuvant and metastatic regimens) allowed, but chemotherapy must have been discontinued at least 14 days and hormonal therapy at least 7 days prior to first study treatment administration
• Prior surgery, whole brain radiotherapy or stereotactic radiosurgery allowed provided that there is unequivocal evidence of one or more new and/or progressive brain metastases after completion of whole brain radiotherapy or stereotactic radiosurgery
• Previous radiotherapy allowed, but radiotherapy must have been discontinued at least 14 days prior to first study treatment administration
• Patients must have recovered to baseline condition or to Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade = 1 from any acute CTCAE v. 5.0 grade =2 side effects of previous treatments
• Without infection of human immunodeficiency virus (HIV) on central laboratory assay results prior to randomization
• Alanine aminotransferase (ALT) </= 2.5 × the upper limit of normal (ULN), Aspartate aminotransferase (AST) </= 2.5 × ULN prior to randomization
• Total bilirubin (TBIL) </= 1.25 × ULN
• Alkaline phosphatase (ALK) </= 2.5 × ULN
• Gamma glutamyl transpeptidase (GGT) </= 2.5 × ULN
• Albumin >/= 30g/L
• Eastern Cooperative Oncology Group (ECOG) performance score of 0 to 2
• A life expectancy of at least 1 month
• Women of child-bearing age should take effective contraceptive measures
• Serum total bilirubin (TBil) </= 1.5 × ULN
• Serum creatinine (Scr) </= 1.5 × ULN
• WBC >/= 3×109/L, Blood neutrophil count >/= 1×109/L, Platelet count >/= 100×109/L, HB >/= 9 g/dL

Exclusion Criteria:

• Lack of histological or cytological confirmation of HER2-positive (IHC 3+ or ISH-positive) breast cancer
• Suffering cerebral hernia
• Only meningeal metastasis
• Earlier exposure to doxorubicin or pirarubicin at a dosage of more than 360 mg/m2
• Earlier exposure to epirubicin at a dosage of more than 900 mg/m2
• Prior treatment with HER2-tyrosine kinase inhibitor other than Lapatinib, Neratinib, Pyrotinib and Tucatinib, such as Afatinib, Erlotinib, Icotinib, Gefitinib and Osimertinib
• Treatment with trastuzumab emtansine within 6 months
• Any other current malignancy or malignancy diagnosed within the past five years (other than carcinoma in situ or stage Ia carcinoma of the cervix, skin basal cell carcinoma and papillary thyroid carcinoma at early stage)
• Active infection with human immunodeficiency virus (HIV) prior to first study treatment administration.
• History of participating any other clinical trials within 30 days prior to randomization
• Known hypersensitivity (Grade 3 or 4) to TDM1 or Afatinib or the excipients of any of the trial drugs
• Significant chronic or recent acute gastrointestinal disorders with diarrhoea as a major symptom e.g. Crohn's disease, malabsorption or Common Terminology Criteria (CTC) grade =2 diarrhoea of any aetiology
• Pregnancy or lactation
• Current severe systemic disease (for example, clinically significant cardiovascular, pulmonary, or renal disease)
• Legal incompetence or limitation.
• Considered unable to complete the study or sign the informed consent due to a medical or mental disorder by the investigator.