The main purpose of this study is to evaluate the safety of ramucirumab plus MEDI4736 in participants with locally advanced and unresectable or metastatic gastrointestinal or thoracic malignancies including gastric or gastroesophageal junction (GEJ) adenocarcinoma, non-small cell lung cancer (NSCLC), or hepatocellular carcinoma (HCC).

Inclusion Criteria:

• Measurable metastatic disease or locally advanced and unresectable disease

  • Has histopathologically confirmed gastric or GEJ adenocarcinoma with documented disease progression after 1-2 prior lines of systemic therapy
  • Has histopathologically confirmed nonsquamous or squamous NSCLC with documented disease progression after 1-3 prior lines of systemic therapy
  • Has histopathologically or cytologically confirmed HCC, Child-Pugh Class A, with documented disease progression during or after discontinuation of sorafenib therapy, or intolerance of sorafenib therapy, and an α-fetoprotein (AFP) ≥ 1.5x upper limit of normal

• Availability of tumor tissue for biomarker analysis

• Has an Eastern Cooperative Oncology Group Performance Status of 0 or 1

• Has adequate organ function

Exclusion Criteria:

• Has known brain metastases
• Has a history of prior cancers not included in this study that were either not treated with curative intent or have been active within the past 5 years
• History of allogeneic organ transplant
• Has active or prior documented autoimmune disease within the past 24 months
• Has human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome (AIDS)-related illness, or a history of immunodeficiency
• Has active hepatitis B or hepatitis C infection, or co-infection with both hepatitis B and C virus
• For gastric/GEJ and NSCLC participants, has chronic hepatitis B or hepatitis C infection. (For HCC participants, those with chronic hepatitis B virus [HBV] infection with a negative HBV deoxyribonucleic acid [DNA] test and who are on antiviral therapy, and those with chronic hepatitis C virus [HCV] infection are eligible)
• Has a history of interstitial lung disease, idiopathic pulmonary fibrosis, pneumoconiosis, non-infections pneumonitis, radiation-induced or drug-induced pneumonitis
• Has received any previous systemic therapy targeting programmed death (PD) 1 or PD-ligand 1/2 signaling pathways, and other immune checkpoint inhibitors
• Have received previous systemic therapy with ramucirumab