The investigators hypothesize that this combination regimen of irinotecan plus ramucirumab administered as second line treatment will be tolerated and lead to improved outcomes similar to paclitaxel plus ramucirumab in patients with advanced gastric and gastro-esophageal junction (GEJ) cancers. This study proposes a phase II clinical trial with irinotecan plus ramucirumab for treatment of patients with metastatic gastric and GEJ adenocarcinoma who have progressed after first line chemotherapy. To the knowledge of the investigators, this regimen has not been previously administered to this patient population, so safety and tolerability will be monitored and reported.