Alisertib in Adults With Nonhematological Malignancies, Followed by Alisertib in Lung, Breast, Head and Neck or Gastroesophageal Malignancies

Inclusion Criteria: Each patient must meet all of the following inclusion criteria to be enrolled in the study: * 18 years or older * Histologically or cytologically confirmed metastatic and/or advanced solid tumor (Phase 1 only) * Phase 2 requires Non-small cell lung cancer (NSCLC); Small-cell lung cancer; Breast adenocarcinoma (female patients only); Squamous cell cancer of the head and neck (HNSCC); or Gastroesophageal adenocarcinoma * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Female patients who are post menopausal, surgically sterile, or agree to practice 2 effective methods of contraception or abstain from heterosexual intercourse * Male patients who agree to practice effective barrier contraception or agree to abstain from heterosexual intercourse * Voluntary written consent * Wiling to comply with scheduled visits, treatment plan, laboratory tests and other trial procedures * Measurable disease (Phase 2 only) Exclusion Criteria: Patients meeting any of the following exclusion criteria are not to be enrolled in the study: * Female patients who are pregnant or lactating * Serious medical or psychiatric illness that could interfere with protocol completion * Receipt of more than 2 previous cytotoxic chemotherapeutic regimens (4 previous regimens for breast cancer). There is no limit on the number of prior noncytotoxic therapies * Prior treatment with Aurora A-targeted agents, including MLN8237 * Prior treatment with high-dose chemotherapy * Prior allogeneic bone marrow or other organ transplant * Antineoplastic therapy, radiation therapy or any experimental therapy 21 days prior to first dose of MLN8237 * Symptomatic brain metastasis * Radiotherapy to greater than 25% of bone marrow * Diagnosis or treatment of another malignancy within 2 years preceding first dose of study drug except nonmelanoma skin cancer or in situ malignancy completely resected * Myocardial infarction within 6 months of enrollment * Uncontrolled cardiovascular condition * Major surgery within 14 days of first dose of MLN8237 * Active infection requiring systemic therapy, or other serious infection * Inability to swallow oral medication * Known history of human immunodeficiency virus (HIV) infection, hepatitis B, or hepatitis C * Patients requiring full systemic anticoagulation * History of uncontrolled sleep apnea syndrome * Treatment with clinically significant enzyme inducers within 14 days prior to the first dose of MLN8237 and during the study