The study is open to all males and females who meet the following inclusion criteria at
        screening and baseline to participate in the study.

        To be included to participate in this study each patient must:

          -  be ≥ 18 years of age;

          -  have an Eastern Cooperative Oncology Group performance status of 0-1 (not declining
             within past 2 weeks, see Appendix 1);

          -  have confirmed HER2 gene amplified tumor fluorescence in-situ hybridization (FISH,
             HER2/cep17 ratio > 2) or HER2 overexpression (IHC 3+) or documented HER2 gene
             mutation. Documentation of HER2 status using FDA approved test(s) for HER2 testing
             specific for HER2 breast and gastric cancer is required prior to screening;

          -  for part 1:

               1. Patients with HER2 positive (defined as documented overexpression or
                  amplification or mutation) metastatic breast cancer who have experienced disease
                  progression following at least 2 prior anti-HER2 therapies for metastatic disease
                  that contain trastuzumab with or without pertuzumab, prior T-DM1, or lapatinib
                  therapy is required;

               2. Patients with HER2 positive metastatic gastric cancer who have disease
                  progression on prior trastuzumab therapy;

               3. other HER2-positive solid tumors (defined as documented overexpression or
                  amplification or mutation) that have no approved targeted agent as standard of
                  care

          -  for part 2:

               1. Patients with HER2 positive metastatic breast cancer who have experienced disease
                  progression after at least 2 prior anti-HER2 therapies for metastatic disease
                  that contain trastuzumab with or without pertuzumab, prior T-DM1, or lapatinib
                  therapy is required;

               2. Patients with documented HER2 mutated NSCLC whose disease progressed on prior
                  therapy;

               3. Patients in Part 2 extension must have at least one measurable lesion as defined
                  by modified Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria;

          -  Left ventricular ejection fraction within institutional limits of normal (by multi
             gated acquisition scan or echocardiography;

          -  have the required screening laboratory values including the following parameters:

               1. Absolute neutrophil count ≥ 1.5×109/L (1,500/mm3);

               2. Platelets ≥ 75×109/L (75,000/mm3);

               3. Hemoglobin ≥ 9.0 g/dL (90 g/L);

               4. Total bilirubin ≤ 1.5× upper limit of normal (ULN);

               5. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5×ULN;
                  for patients with liver metastases, ALT and AST ≤ 5×ULN;

               6. Serum creatinine ≤ 1.5×ULN;

          -  have a life expectancy of > 12 weeks;

          -  for female patients who are of child bearing potential, a negative serum pregnancy
             test result before study entry. A female patient of childbearing potential is one who
             is biologically capable of becoming pregnant. This includes women who are using
             contraceptives or other means of birth control or whose sexual partners are either
             sterile or using contraceptives;

          -  and who have provided informed consent by signing the informed consent form.

        Main Exclusion Criteria:

        Patients who meet any of the criteria listed below will not be eligible for participation
        in this study. A patient will not be eligible for study participation if:

          -  is unable or unwilling to swallow pyrotinib;

          -  has been < 2 weeks since the last radiotherapy, chemotherapy, hormone therapy, surgery
             or molecule-target therapy (< 6 weeks if chemotherapy included nitrosoureas or
             mitomycin);

          -  the bone or skin is the only site of disease (for Part 2 extension only);

          -  has pleural or peritoneal only disease;

          -  has uncontrolled ≥ grade 2 hypokalemia and hypomagnesemia;

          -  has had other cancer(s) within 5 years prior to screening with the exception of
             contralateral breast carcinoma, adequately treated cervical carcinoma in situ, or
             adequately treated basal or squamous cell carcinoma of the skin;

          -  has active central nervous system (CNS) metastases, as indicated by clinical symptoms,
             cerebral edema, and/or progressive growth (patients with a history of CNS metastases
             or cord compression are allowable if they have been definitively treated and have been
             clinically stable for at least 4 weeks, and off steroids and anticonvulsants, before
             first dose of study drug);

          -  has either QTcF prolongation (> 470 ms for female and > 450 ms for male), a known
             history of QTcF prolongation or Torsade de Pointes; or is on drugs that are required
             for existing medical conditions and that may result in QT prolongation (e.g.,
             anti-arrhythmic drugs); patients who use medications that have a minimal impact on the
             QTcF interval in the Arizona-CERT criteria are allowed to participate in this study at
             Investigator's discretion based on his/her clinical assessment);

          -  has a significant chronic or recent acute gastrointestinal disorder with diarrhea as a
             major symptom (e.g., Crohn's disease, malabsorption, or ≥ grade 2 diarrhea of any
             etiology at baseline);

          -  has participated in any other investigational drug clinical studies within the last 4
             weeks;

          -  is concurrently receiving other anti-tumor therapies at time of study screening visit;

          -  has an active infection (per Investigator judgment);

          -  has a history of immunodeficiency including seropositive for human immunodeficiency
             virus, or has other acquired or congenital immunodeficient disease;

          -  has evidence of uncontrolled heart disease, including (1) congestive heart failure
             (New York Heart Association functional classification) of ≥ 2), (2) angina requiring
             treatment (3) myocardial infarction within the past 12 months, or (4) any clinically
             significant supraventricular arrhythmia or ventricular arrhythmia requiring treatment
             or intervention;

          -  has allergies or a known history of hypersensitivity to any components of the
             pyrotinib;

          -  is female and of childbearing potential (WOCBP) who is unwilling or unable to use an
             acceptable method (barrier methods only) to avoid pregnancy for the entire study
             period and for up to 28 days post last dose;

          -  is female and pregnant (or found to be pregnant at screening) or breastfeeding;

          -  evidence of significant medical illness or an abnormal laboratory finding, which
             according to the Investigator's judgment, will substantially increase the risk of
             participation in and completion of the study. Including, but not limited to, serious
             ongoing infection (ie, requiring intravenous antibiotic or antiviral agent),
             uncontrolled major seizure disorder, or significant pulmonary disorder (e.g.
             interstitial pneumonitis, pulmonary hypertension); hypertension (> grade 3), severe
             diabetes (uncontrolled > grade 3 hyperglycemia), serious ongoing infection or thyroid
             disease;

          -  has a known history of neurological psychiatric disease including epilepsy or dementia
             that would interfere with patient's ability to participate in the study or to provide
             consent;

          -  has had prior exposure to any other investigational HER2 targeted agents within 4
             weeks of screening visit.

          -  is currently taking strong CYP3A4 inhibitor or concomitant meds.