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Inclusion Criteria:

1. Having provided written informed consent, and be able to follow clinical trial protocol.
2. Men or women aged 18-75.
3. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1，life expectancy greater than 3 months.
4. Left ventricular ejection fraction (LVEF) ≥50%.
5. Histopathological and/or cytological confirmed Her2-positive locally advanced or metastatic breast cancer (IHC3+, or IHC2+ and ISH+), \*ISH: Fluorescence in situ hybridization (FISH) or dual in situ hybridization (DISH); ISH positivity is defined as a ratio of HER2 gene copy number to CEP17 signal number ≥2.0. When the immunohistochemical (IHC) result is 3+, ISH testing is not required. When the IHC result is 2+, ISH testing should be performed to confirm HER2 positivity.
6. Failure for at least 1 line of standard systemic treatment for metastatic disease. Meet one of the following conditions:

   1. Recurrent within 12 months after completing or during neoadjuvant/ adjuvant therapy (the regimens contain trastuzumab or its biosimilar with pertuzumab or not).
   2. Received at least one treatment with trastuzumab or its biosimilar ±pertuzumab (monotherapy or in combination with other drugs) for recurrent or metastatic disease.
7. Having at least one measurable lesion according to RECIST 1.1.
8. Previous exposure to taxanes.
9. During the screening period and the first 7 days before treatment, the following indicators confirm appropriate organ functions:

   1. Hematology: WBC≥3.0×109/L；NE≥1.5×109/L；Hb≥90 g/L；Plt≥100×109/L;
   2. Liver function: Total bilirubin ≤ 1.5 x the upper limit of normal; AST and ALT ≤ 2.5 x the upper limit of normal, ≤ 5.0 x the upper limit of normal in the presence of liver metastases;
   3. Kidney function: Serum creatinine ≤1.5 x the upper limit of normal;
   4. Coagulation function: prothrombin time and activated partial thromboplastin time ≤1.5 x the upper limit of normal.
10. Adequate wash-out periods:

    1. Major surgery ≥4 weeks;
    2. Radiotherapy ≥4 weeks (Palliative stereotactic radiotherapy without abdominal involvement radiotherapy: ≥2 weeks);
    3. Autologous transplantation: ≥3 months
    4. targeted therapy or chemotherapy≥4 weeks;
    5. Radioactive particle therapy: ≥3 months
    6. Nuclide therapy: ≥3 months
    7. Hormone therapy: ≥2 weeks, or based on judgement on the breast cancer
    8. Participants from the investigators' judgment;
    9. Endocrine therapy: ≥4weeks;
    10. Chemotherapy or targeted therapy: 5-fluorouracil-based preparations, folinic acid preparations, and/or Weekly paclitaxel: ≥2 weeks;
    11. Tyrosine kinase inhibitor: ≥2 weeks (or 5 half-lives)
    12. In the case of a decline period, the longer one shall prevail;
    13. Nitrosoureas or mitomycin C: ≥6 weeks
    14. Immunotherapy ≥4 weeks;
    15. Potent CYP3A4 inhibitor≥3\*t1/2 weeks;
    16. Any investigational agents≥4 weeks.
11. Female subjects who are capable of bearing children must have negative urine or serum pregnancy test results within 7 days before randomization, and must commit to using contraception throughout the study period and continue to do so for 7 months after the study ends.

Exclusion Criteria:

1. Clinical symptomatic brain metastasis is defined as untreated and symptomatic, or requiring steroid or anticonvulsant treatment to control related symptoms. Patients with asymptomatic brain metastasis, or with stable clinical symptoms and no need for steroid hormone and other treatments for brain metastasis for ≥28 days, can be enrolled.
2. Have previously been treated with: another antibody-drug conjugate (ADC) consisting of DM1 or its derivative，pyrotinib and capecitabine，except for the following situations:

   1. During (neo)adjuvant therapy, received pyrotinib, and the participants who have experienced recurrence or metastasis more than 6 months after the last treatment and have not received pirlotinib since then are allowed to be enrolled;
   2. Participants who have received pirlotinib treatment during the recurrent and metastatic stage, discontinued the medication due to reasons other than disease progression, and have progressed more than 6 months after discontinuation are allowed to be enrolled;
   3. Participants who have received treatment with ADC drugs with different small molecule toxins (such as DS-8201, GQ1005, SHR-A1811, etc.) are eligible for enrollment. Such patients are also allowed to have received pirlotinib treatment during the recurrent or metastatic stage, and those who have progressed after more than 6 months of pirlotinib treatment are also eligible for enrollment.
3. Have other malignant tumors within 5 years before signing the informed consent form ( except for cured skin basal cell carcinoma and cervical carcinoma in situ).
4. Have a medical history of myocardial infarction or clinically significant heart diseases, including but not limited to,

   1. symptomatic congestive heart failure (CHF) (NYHA classes II-IV), or serious cardiac arrhythmia which required to therapy;
   2. Having a history of myocardial infarction or unstable angina pectoris within 6 months prior to the initial treatment,
   3. Have a corrected QT interval (QTc) prolongation to \> 450 milliseconds (ms) in males and \> 470 ms in females.
5. Have clinically significant acute and chronic pulmonary diseases (e.g. interstitial lung disease (ILD), lung infection, pulmonary fibrosis, and severe radiation pneumonitis), participants with a history of ILD/non-infectious pneumonia requiring hormone therapy, or suspected of having lung diseases based on imaging examination at screening, with imaging suggesting miliary disseminated metastasis, subjects with specific pulmonary complications including but not limited to any potential lung diseases (such as pulmonary embolism, severe asthma, severe chronic obstructive pulmonary disease, restrictive lung disease, or other conditions that may interfere with the detection or management of drug-related pulmonary toxicity within 3 months prior to enrollment in the study), or subjects requiring oxygen therapy.
6. History of allergic reaction to any component of GQ1001.
7. The toxicity of previous anti-cancer therapy has not recovered to ≤1 as specified in CTCAE v5.0 (except for hair loss); e.g. chronic grade 2 toxicity might be determined per the investigator's judgment.
8. The cumulative dose of anthracyclines or equivalent\>500 mg/m2.
9. Uncontrollable infections require intravenous antibiotics, antiviral drugs, or antifungal drugs.
10. Hepatitis B virus (HBV) infection (including hepatitis B surface antigen \[HBsAg\] positive or hepatitis B core antibody \[HBcAb\] positive and HBV DNA positive); HIV, syphilis, hepatitis C antibody positive, or other severe and fatal viral or bacterial diseases, except for patients with stable hepatitis B (HBV viral copy number below the upper limit of reference value) after drug treatment and cured hepatitis C patients (HCV viral copy number below the detection limit of assay method).
11. Per the investigator's judgment, participants with any history or current evidence of concomitant disease treatment or laboratory abnormalities may interfere with the trial results, as well as their participation and compliance.
12. Lactating women or women who have confirmed pregnancy through a pregnancy test within 7 days prior to their first treatment.
13. Male or female subjects unwilling to use approved contraceptive methods (e.g. birth control pills, barrier device, intrauterine device, abstinence) during the study and for 7 months following the last dose of the study drug infusion.
14. Other circumstances that are deemed not appropriate for the study.
15. Inability to swallow, chronic diarrhea and intestinal obstruction, or other factors that affect drug administration and absorption.

• Shanghai, Shanghai Municipality, China