A Study of TRK-950 When Used in Combination With Ramucirumab and Paclitaxel in Patients With Gastric Cancer

Inclusion Criteria: * Histologically or cytologically confirmed metastatic, or locally advanced and unresectable gastric or GEJ adenocarcinoma. * The patient is eligible to receive Ramucirumab + Paclitaxel. * Documented objective radiographic or clinical disease progression (e.g., any new or worsening malignant effusion documented by ultrasound examination) which may be confirmed by pathologic criteria (histology and/or cytology) if appropriate, during or after treatment. The prior treatment must meet one of the following criteria with the following treatment history: 1. First treatment for metastatic disease or locally advanced disease without experiencing adjuvant / neo-adjuvant treatment, which progressed during treatment or within 4 months after the last dose of treatment 2. Adjuvant / neo-adjuvant treatment which progressed more than 6 months after the last dose of treatment and first treatment for metastatic disease or locally advanced disease, which progressed during the treatment or within 4 months after the last dose of treatment 3. Adjuvant / neo-adjuvant treatment which progressed during treatment or within 6 months after the last dose of treatment 4. Adjuvant / neo-adjuvant treatment which progressed during treatment or within 6 months after the last dose of treatment and first treatment for metastatic disease or locally advanced disease, which progressed during treatment or within 4 months after the last dose of treatment * Presence of primary or metastatic disease, measurable per RECIST v1.1 on CT scan. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. * Life expectancy of at least 3 months. * Age ≥ 18 years in the US and Japan, and ≥ 19 years of age in Korea. * Signed, written IRB-approved informed consent. * Adequate organ function from specimens collected within 14 days prior to Day 1. * For men and women of child-producing potential, the use of effective contraceptive methods during the study and for 6 months after the last dose of TRK-950. * All patients must sign a pre-screening consent to assess tumor tissue to determine eligibility. Tumor tissue must be evaluable for CAPRIN-1 staining at a CLIA certified laboratory and meet or exceed the cutoff value (30% at ≥ 2+ staining) as defined in the expression level requirements. Exclusion Criteria: * Prior history of treatment with ramucirumab or paclitaxel. * HER2 positive gastric or GEJ adenocarcinoma. * Major surgery within 28 days prior to randomization. * Baseline corrected QT (QTc) interval of \> 470 msec for females and \> 450 msec for males calculated using Fridericia's formula. * New York Heart Association (NYHA) Class II - IV symptomatic congestive heart failure, or symptomatic or poorly controlled cardiac arrhythmia. * The patient has experienced any arterial thrombotic event, including myocardial infarction, unstable angina, cerebrovascular accident, or transient ischemic attack, within 3 months prior to randomization. * The patient has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Clinically symptomatic venous thromboembolism or current treatment with anti-coagulants. (Patients receiving prophylactic and low-dose anticoagulation therapy are eligible provided that the coagulation parameter defined in the Inclusion Criterion 9 is met.) * Uncontrolled arterial hypertension ≥ 150 mmHg (systolic) or ≥ 90 mmHg (diastolic) despite standard medical management. * Active, uncontrolled bacterial, viral, or fungal infections, requiring systemic therapy. * Pregnant or nursing women. * Treatment with radiation therapy within 2 weeks, or treatment with chemotherapy, immunotherapy, targeted therapy, or investigational therapy within 4 weeks prior to randomization (within 2 weeks for Oral FU (S1 and capecitabine)). * The patient has significant bleeding disorders, vasculitis, or had a significant bleeding episode from the gastrointestinal tract within 3 months prior to randomization. * Clinically significant ascites, paracentesis in the last 3 months, or undergoes regular paracentesis procedures. * History of gastrointestinal perforation and/or fistulae within 6 months prior to randomization. * The patient has a serious or non-healing wound, peptic ulcer, or bone fracture within 28 days prior to randomization. * The patient has a bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection (e.g., hemicolectomy or extensive small intestine resection with chronic diarrhea), Crohn's disease, ulcerative colitis, or chronic diarrhea. * Known active infection with HIV, hepatitis B or hepatitis C. Patients with a history of hepatitis B or C are allowed if HBV DNA or Hep C RNA are undetectable. * The patient is currently enrolled in a clinical trial involving an investigational product or non-approved use of a drug, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study. Patients who have recently discontinued dosing of study drug are eligible to participate as long as the final dose of study drug was ≥ 28 days from randomization for participation in this study. Patients participating in surveys or observational studies are eligible to participate in this study.