Patient description: The patient is a 45-year-old postmenopausal woman with cytologically confirmed breast cancer. A core biopsy revealed a 3 cm invasive ductal breast carcinoma in the left upper outer quadrant. The tumor is HER2-positive and ER/PR negative. Axillary sampling revealed 5 positive lymph nodes. CXR was remarkable for metastatic lesions. The patient is using multivitamins and iron supplements. She does not smoke or consume alcohol. She is not sexually active and has no children. She is a candidate for tumor resection and agrees to do so prior to chemotherapy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Advanced Solid Tumor Breast Neoplasms Have given written informed consent prior to any study specific procedures. 2. Male or female, aged ≥18 years. 3. Subjects with advanced solid tumors Phase 1: Histologically or cytologically confirmed, locally advanced (not amenable to curative treatment of surgical resection or radiation therapy), recurrent, or metastatic solid tumors that were refractory to standard therapy or for which no standard-of-care therapy Phase 2a Cohort A: HR+/HER2 locally advanced, recurrent, or metastatic breast cancer with disease progression after first-line endocrine therapy (not fulvestrant) or intolerant of it, histologically confirmed by the primary and/or metastatic lesions, not amenable to chemotherapy or curative treatment of surgical resection or radiation therapy; if the pathology of the primary and metastatic lesions are inconsistent, diagnosis should be based on metastatic lesions' pathology Phase 2a Cohort B: HR+/HER2 locally advanced, recurrent, or metastatic breast cancer with no prior systemic therapy in this disease setting or relapse more than 1 years from completion of adjuvant endocrine therapy, histologically confirmed by the primary and/or metastatic lesions, not amenable to chemotherapy or curative treatment of surgical resection or radiation therapy; if the pathology of the primary and metastatic lesions are inconsistent, diagnosis should be based on metastatic lesions' pathology. 4. At least 1 measurable lesion based on the v1.1 criteria. 5. Life expectancy≥ 12 weeks. 6. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS)≤1. 7. Adequate bone marrow and organ function, defined as following: 1. absolute neutrophil count≥1.5×10^9/L, platelets≥100×10^9/L, hemoglobin≥100 g/L; 2. total bilirubin≤1.5×ULN(≤3×ULN for Gilbert syndrome), alanine aminotransferase and aspartate aminotransferase≤3×ULN; 3. serum creatinine≤1.5×ULN or a creatinine clearance calculated by Cockcroft-Gault formula≥50 mL/min; urinary protein measured by semi-quantitative method<2+; if urinary protein measured by semi-quantitative method at baseline ≥2+, 24-h urinary protein<1g; 4. activated partial thromboplastin time and international normalized ratio≤1.5×ULN; 5. LVEF≥50%; 6. Corrected QT interval (QTcF)<450ms for men and <470ms for women at resting. 8. Female subjects should take effective contraceptive methods during the study and for 60 days after the last dose of BPI-1178, and must have a negative pregnancy test prior to dosing if of child-bearing potential, or must have evidence of non-child-bearing potential; male subjects should take effective contraceptive methods during the study and for 120 days after the last dose of BPI-1178. 9. All subjects must have enough mental behavior ability, understand the nature and significance of the study, as well as the risks associated with the study  Currently receiving or have received any CDK4/6 inhibitors. 2. Have had allergies or history of severe allergies. 3. Have participated in any clinical trials within 4 weeks prior to the dosing of BPI-1178. 4. Have received last dose of anti-cancer treatment (chemotherapy, endocrine therapy, targeted therapy, immunotherapy or embolization therapy, etc.) within 4 weeks prior to the dosing of BPI-1178; have received last dose of biological products (if endocrine therapy, within 4 weeks prior to the dosing of BPI-1178), nitrosourea or mitomycin C within 6 weeks prior to the dosing of BPI-1178; (except GnRHa treatment for pre/peri-menopausal subjects in phase 2a study). 5. Any toxicity related to previous treatment before enrollment defined by CTCAE (v5.0) Grade≥2 (except hair loss). 6. Presence of third interstitial fluid that cannot be controlled by drainage or other methods (such as large amounts of pleural fluid and ascites). 7. Requiring long-term treatment of steroid. 8. Having uncorrectable hypokalemia and hypomagnesemia at enrollment. 9. Any of the following any cardiac rhythm and conduction abnormalities with clinical significance, such as atrial fibrillation, complete left bundle branch block, 3rd-degree atrioventricular block, 2nd-degree atrioventricular block, PR interval>250ms; any risk of QT interval prolongation and arrhythmia, such as symptomatic heart failure-New York Heart Association (NYHA) grades II～ IV, congenital long QT syndrome, Brugada syndrome, history of QT interval prolongation (male>470ms, female>480ms) or history of torsade de pointes, family history of long QT syndrome or sudden death with unknown cause before 40 years old in the first-degree relatives, any concomitant medications that may prolong QT interval; any following diseases within 6 months prior to the dosing of BPI-1178: unstable angina pectoris, myocardial infarction, coronary heart disease, cerebrovascular events, pulmonary embolism, or cardiac revascularization,etc.. 10. Have active infection, such as hepatitis B (HBsAg positive and hepatitis B virus DNA≥1×10^3 copy/ml), hepatitis C and human immunodeficiency virus (HIV) infection. 11. Have a history of allogeneic organ transplantation and allogeneic hematopoietic stem cell transplantation. 12. Any factors, in the judgment of the investigator, that may affect the administration and absorption of BPI-1178 (for example, uncontrolled inflammatory gastrointestinal diseases, abdominal fistula or gastrointestinal perforation within 6 months, extensive resection of small intestinal, with tube feeding or parenteral nutrition, inability to swallow, chronic diarrhea, and intestinal obstruction). 13. Have spinal cord compression, metastases of the meninges, or brain metastases with obvious symptoms. The following cases of brain metastases without symptoms can be enrolled: brain metastases without obvious symptoms diagnosed at screening visit, steroids and/or local treatment not required judged by investigator; brain metastases without obvious symptoms after local treatment (such as radiotherapy), and steroids and/or antiepileptic therapy has stopped for at least 7 days before the first dosing of BPI-1178. 14. In the judgment of the investigator, have a concomitant disease (such as severe hypertension, diabetes, thyroid disease, severe infection, portal hypertension, cirrhosis, etc.) that would endanger the subjects' safety or affect the completion of the study. 15. Have had major surgery (craniotomy, thoracotomy, or laparotomy) or unhealed wounds, ulcers, or fractures within 4 weeks prior to the dosing of BPI-1178. 16. Pregnant or lactating women, or fertile women with pregnancy test positive at baseline. 17. Any factors that may endanger subject's safety and may affect subject's compliance with the study. 18. Drug abuse, alcoholic addiction, medical and mental illness and social barriers judged by investigator, which may interfere the subjects' participation in the study or affect the evaluation of study endpoints . Any factor that investigator believes may make the subjects not suitable to receive BPI-1178. Subjects are unwilling or unable to comply with the requirements of the study protocol