Inclusion Criteria:

1. Patients must have the ability to understand and the willingness to sign a written informed consent document 2 Patients must be willing and able to comply with the scheduled visits, treatment plan, laboratory tests and other specified study procedures 3. Age ≥18, male or female 4.Dose escalation: locally advanced or metastatic solid tumors Dose expansion: Advanced or metastatic EGFR-mutant NSCLC 5. Patients must have measurable disease by RECIST v1.1. 6. Patients must have an ECOG performance status (PS) ≤2 7.Patients with a life expectancy of ≥12 weeks. 8. Patients must have adequate organ function

Exclusion Criteria:

1. Patients with a known additional malignancy that is progressing or requires active treatment
2. Patients who have previously received a SHP-2 inhibitor
3. Patients who are hypersensitivity to SHP-2 inhibitor or any ingredients
4. Treatment with any of the related anti-cancer therapies prior to the first dose of BBP-398 within the stated timeframes
5. Patients with known active Hepatitis B, Hepatitis C infection, or HIV infection.
6. Patients with any of the cardiac-related issues or findings
7. Patients with a history of CVA, myocardial infarction or unstable angina within the previous 6 months before starting therapy.
8. Patients with known central nervous system (CNS) tumors
9. Patients with known active CNS metastases and/or carcinomatous meningitis.
10. Patients with persisting toxicity related to prior therapy.
11. Patients who have undergone major surgery within 4 weeks prior to study enrollment.
12. Pregnant or breastfeeding female patients.
13. Patients with inability to swallow oral medications or with gastrointestinal illness that would preclude the absorption of an oral agent.