The main purpose of this study is to evaluate the effectiveness of LY2875358 in participants with MET diagnostic positive (+), advanced gastric or gastroesophageal junction (GEJ) cancer.

Inclusion Criteria:

• Have a diagnosis of a histopathologically or cytologically confirmed local and/or advanced gastric or gastroesophageal junction (GEJ) adenocarcinoma which is unresectable
• Have received 2 regimens of prior chemotherapies for gastric or GEJ adenocarcinoma
• Have the presence of measurable disease as defined by the Response Evaluation Criteria in Solid Tumors (RECIST 1.1)
• Have consent to provide a tissue sample for pre-screening
• Determined to be MET diagnostic positive based upon testing of a tumor sample obtained at any time before enrollment
• Have discontinued all previous treatments for cancer, including chemotherapy and radiotherapy, for at least 3 weeks before enrollment and have recovered from the acute effects of therapy
• Have adequate organ function
• Male participants: must agree to use a reliable method of birth control and to not donate sperm during the study and for at least 4 months following last dose of study drug or country requirements, whichever is longer
• Female participants: are women of child-bearing potential who test negative for pregnancy ≤14 days before enrollment based on a serum pregnancy test and agree to use a reliable method of birth control during the study and for 4 months following the last dose of the study drug and must also not be breastfeeding
• Have a performance status of ≤1 on the Eastern Cooperative Oncology Group (ECOG) scale
• Have an estimated life expectancy, in the judgment of the investigator, of at least 12 weeks

Exclusion Criteria:

• Are currently enrolled in, or discontinued within the last 21 days from, a clinical trial involving an investigational product or non-approved use of a drug or device, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study
• Have previously completed or withdrawn from this study or any other study investigating LY2875358
• Have an active fungal, bacterial, and/or known viral infection
• Have a history of New York Heart Association class ≥3, unstable angina, myocardial infarction (MI) in 6 months prior to study drug administration
• Have symptomatic central nervous system (CNS) malignancy or metastasis
• Have previous or concurrent malignancies
• Have received a liver transplant, or have liver cirrhosis with a Child-Pugh Stage of B or C
• Have corrected QT interval (QTc) of >470 millisecond (msec) on screening electrocardiogram (ECG)
• Have received previous treatment with any hepatocyte growth factor (HGF)/MET targeting therapeutics
• Have a history of radiation therapy involving more than 25% of the bone marrow. Previous radiation therapy is allowed but should have been limited and must not have included whole pelvis radiation