Two-Part, Phase Ib/II, Open Label, Single-Arm, Multi-center Study to Evaluate the Safety and Efficacy of Varlitinib in Combination With Weekly Paclitaxel in EGFR/HER2 Co-expressing Advanced or Metastatic Gastric Cancer Patients

Inclusion Criteria: 1. Capable of understanding and complying with the requirements of the study and have signed the Informed Consent Form (ICF). 2. Able to communicate well with the Investigator and understand and comply with the requirements of the study. 3. Has a histologically or cytologically confirmed diagnosis of advanced or metastatic gastric adenocarcinoma (systemic metastasis or locally advanced unresectable gastric cancer). A subject must have previously received 1st line chemotherapy including fluoropyrimidine and/or platinum and have showed progression. 4. Not received paclitaxel-based chemotherapy previously. 5. Has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or1 6. Has a measurable or evaluable disease as determined by RECIST 1.1 criteria. 7. Able to swallow orally administered medication. 8. Life expectancy of at least 3 months 9. Has an adequate baseline organ function defined as: * White blood cells ≥3000/mm3 and neutrophils ≥1500/mm3 * Platelets ≥100000/mm3 * Hemoglobin ≥9.0 g/dL * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤3.0 × upper limit of normal (ULN) of the study site (or ≤5.0 × ULN in patients with liver metastases) * Total bilirubin ≤2.0 × ULN * Creatinine≤1.5 × ULN or creatinine clearance (either measured value or estimated value using the Cockcroft-Gault equation) \>60ml/min. Part 1, Phase Ib 11.Subjects will be included regardless of EGFR and HER-2 Status Part 2, Phase II 12\. Provision of an unstained, archived tumor tissue sample in a quantity sufficient to allow for central analysis of EGFR and HER2 expression status. 13\. Tumours with immunohistochemistry (IHC) evidence of expression of HER1 (at level of +, or ++, or +++) and HER-2 (at level of +, or ++, or +++) using standard criteria. Also, Subjects with HER-2 IHC (at level of +, or ++, or +++) and EGFR gene amplification/ mutation by NGS are included. Exclusion Criteria: 1. Has multiple cancers (with the exception of completely resected basal cell carcinoma, stage I squamous cell carcinoma, carcinoma in situ, intramucosal carcinoma, and superficial bladder cancer, and any other cancers that have not recurred for at least 5 years) 2. Has a current or past history of interstitial lung disease or pulmonary fibrosis diagnosed on imaging (preferably CT) or clinical findings 3. Has brain or leptomeningeal metastases. Patients may be randomized for the study if they are asymptomatic and require no treatment. 4. History of uncontrollable or significant cardiovascular disease meeting any of the following; * myocardial infarction within 180 days before study enrolment * uncontrolled angina pectoris within 180 days before study enrolment * New York Heart Association (NYHA) Class III or IV congestive heart failure * uncontrolled hypertension despite appropriate treatment (e.g., systolic blood pressure ≥150mmHg or diastolic blood pressure ≥90 mmHg lasting 24 hours or more) * arrhythmia requiring treatment * baseline corrected QT interval (Fridericia"s formula) (QTcF) \> 450 ms or patients with known long QT syndrome; torsade de pointes 5. Has an active systemic infection requiring treatment. 6. Has a contraindication to paclitaxel. 7. Has undergone surgery (any surgery involving general anesthesia) within 28 days before study treatment. 8. Subjects with malabsorption syndrome, diseases significantly affecting gastrointestinal function, has total gastrectomy, or difficulty in swallowing and retaining oral medications. 9. Has received radiotherapy for gastric cancer within 28 days before treatment or radiotherapy for bone metastases within 14 days before treatment 10. Positive test result for human immunodeficiency virus-1 (HIV-1) antibody, Hepatitis B surface protein (HBs) antigen and HBV titer\>2000 IU/ml (10,000 copy/ml), or hepatitis C virus (HCV) antibody positive result 11. Any unresolved Grade 2 (per CTCAE v4.0) toxicity from previous anti-cancer therapy at the time of enrollment such as neuropathy, except alopecia or anemia 12. Previously treated with varlitinib 13. Unable to comply to the study protocol 14. Have participated in a study involving another investigational drug within 21 days prior to the first dose of study drug 15. Has a history of drug hypersensitivity reactions or hypersensitivity to drugs chemically related to the study drug.