MLN1117 in Combination With Docetaxel, Paclitaxel, and Other Investigational Anticancer Agents to Treat Participants With Gastric and Gastroesophageal Adenocarcinoma

The drug being tested in this study is called MLN1117. MLN1117 is being tested to treat people who have locally advanced or metastatic gastric or gastroesophageal junction adenocarcinoma. This study will look at the dose-limiting toxicity and response to treatment in participants who take MLN1117 in combination with TAK-659, alisertib, paclitaxel, or docetaxel. The study will enroll 32 participants in the dose escalation phase (Part 1) and 118 participants in the dose expansion phase (Part 2). Participants will be assigned to 1 of the 7 treatment groups: * MLN1117 300 mg+Alisertib * MLN1117 600 mg+Alisertib * MLN1117 300 mg+Paclitaxel * MLN1117 600 mg+Paclitaxel * MLN1117 300 mg+TAK-659 * MLN1117 200 mg+Docetaxel * MLN1117 300 mg+Docetaxel In Part 1, the dose of MLN1117 will be increased step by step. All participants will be asked to take tablets of MLN1117 for 3 days on and 4 days off per week in 28-day treatment cycles or 21-day treatment cycles when given in combination with the other companion drugs. This multi-center trial will be conducted in Spain and United States. The overall time to participate in this study is 10 months for Part 1 and 24 months for Part 2. Participants will make multiple visits to the clinic, and be contacted by telephone, e-mail or mail every 12 weeks for up to 6 months or 1 year after the last dose of study drug for a follow-up assessment.