This clinical trial is to evaluate the efficacy and safety of subjects with metastatic gastric adenocarcinoma or adenocarcinoma of the gastroesophageal junction. In addition, this clinical trial is performed to analyze the genome-specific response rate and genome analysis to identify predictive markers that respond to investigational drug administration.

4 weeks (28 days) administration is considered as 1 cycle.

[Bactosertib／TEW-7197] A 300mg dose is administered orally as tablets twice a day for 5 days, followed by a 2 day holiday. (5 days medication/2 days off). All doses are taken in the morning/evening, approximately 12 hours apart, regardless of food.

[Ramucirumab (ramucirumab)] A dose of 8 mg/kg (8 mg per kg of body weight) is administered once for 60 minutes at the 1st and 15th days of each cycle. This drug is administered directly into a blood vessel using an infusion pump.

[paclitaxel (paclitaxel)] A dose of 80mg/m2 is administered intravenously for 60 minutes at the 1st, 8th, and 15th days of each cycle and is withdrawn for 1 week.

Inclusion Criteria:

1. Patients with histologically or cytologically confirmed gastric cancer, including gastric adenocarcinoma or GEJ adenocarcinoma.
2. Patients with metastatic or locally recurrent unresectable disease.
3. Patients with diseased lesions that can be measured using standard computed tomography (CT) or magnetic resonance imaging (MRI).
4. Patients who have experienced disease progression during or after primary therapy for metastatic disease.
5. Patients over 19 years of age.
6. All clinically significant toxic effects of previous chemotherapy, surgery, radiation therapy, or hormone therapy are rated ≤1 (or neuropathic Cases ≤2 grade) (excluding hair loss).
7. Patients with an Eastern Oncology Cooperative Group Performance Status (ECOG PS) score of 0 or 1.
8. Total bilirubin ≤1.5 mg/dL (25.65 µmol/L), and aspartic acid aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 x upper limit of normal (ULN; or 5.0 x with liver metastasis) Patients with adequate liver function as defined by ULN).

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Exclusion Criteria:

1. Patients previously receiving treatment targeting the TGF-β signaling pathway
2. Patients who previously received Taxane-based chemotherapy
3. Patients with recorded and/or symptomatic brain or meningeal metastases.
4. Patients who experienced Grade 3-4 GI bleeding within 3 months prior to enrollment.
5. Patients who have experienced arterial thromboembolic events including, but not limited to, myocardial infarction, transient ischemic attack, cerebrovascular attack, or unstable angina within 6 months prior to enrollment.
6. Ongoing or active infection, symptomatic congestive heart failure, unstable angina, symptomatic or poorly controlled cardiac arrhythmias, uncontrolled thrombotic or hemorrhagic disease, interstitial pneumonia or pulmonary fibrosis, or in the judgment of the treating physician. Patients with other serious medical conditions that are not controlled.
7. Patients with ongoing or active psychiatric conditions or social situations that may limit adherence to treatment.
8. Patients with uncontrolled or poorly controlled hypertension (systolic >160 mmHg or diastolic >100 mmHg for >4 weeks) despite standard medical care.