Alisertib (MLN8237) in Combination With Weekly Paclitaxel in East Asian Patients With Advanced Solid Tumors

Inclusion Criteria: 1. Male or female participants 18 years or older (or minimum age of legal consent consistent with local regulations) at the time written study informed consent is obtained. 2. Participants of East Asian ethnicity (eg, Chinese, Japanese, or Korean). 3. Must have a diagnosis of a solid tumor malignancy (escalation part) or relapsed or refractory ovarian cancer (OC) or small cell lung cancer (SCLC) (expansion part). * Participants in the expansion cohort must have a pathologically (histology or cytology) confirmed diagnosis of either OC (including recurrent epithelial ovarian, fallopian tube, or primary peritoneal cancer) or SCLC, which is measurable disease as per Response Evaluation Criteria in Solid Tumors (RECIST), version 1.1. * Participants in the expansion cohort must not have received more than 2 prior taxane containing regimens. 4. No antineoplastic therapy (eg, drugs, biologicals, monoclonal antibodies, etc) or radiotherapy within the 3 weeks before enrollment (14 days for regimens with recovery expected within 7 to 14 days). The participant must have recovered (ie, ≤ Grade 1 toxicity or participant's baseline status, except alopecia) from all treatment-related toxicities. 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 6. Adequate bone marrow function as defined by: * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm3 (without need for growth factor support). * Platelet count ≥ 100,000 cells/mm3 (without need for transfusion or growth factor support). * Hemoglobin level ≥ 9 g/dL. 7. Adequate liver function as defined by: * Bilirubin \< 1.5 times the upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 x ULN (≤ 5 x ULN if due to liver metastases) * Serum albumin equal to or greater than the lower limit of normal 8. Adequate renal function as defined by: * Creatinine clearance ≥ 30 mL/minute (can be calculated using serum creatinine value). 9. No more than 2 previous chemotherapy regimen in the metastatic setting. 10. Female participants who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 30 days after the last dose of study drug * Adhere to any treatment-specific pregnancy prevention guidelines for paclitaxel Male participants, even if surgically sterilized (ie, status postvasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug * Adhere to any treatment-specific pregnancy prevention guidelines for paclitaxel. 11. Voluntary written consent must be given before performance of any study-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to future medical care. 12. Suitable venous access for the study-required blood sampling, including pharmacokinetics (PK). 13. Ability to swallow tablets. Exclusion Criteria: 1. Participants with carcinomatous meningitis. 2. Participants with symptomatic and/or progressive brain metastases or treatment with brain edema. 3. Known hypersensitivity to Cremophor® EL, paclitaxel, alisertib or their components. 4. Prior treatment with an Aurora A specific-targeted or pan-Aurora-targeted agent, including alisertib in any setting. 5. Prior history of ≥ Grade 2 neurotoxicity or any toxicity requiring discontinuation from taxane chemotherapy that is not resolved to ≤ Grade 1. 6. Participants who received prior weekly taxane-based therapy with early disease progression during or within 1 month of completing therapy (refractory disease). 7. Any comorbid condition or unresolved toxicity that would preclude administration of weekly paclitaxel. 8. Systemic treatment with moderate or strong CYP3A inhibitors must be discontinued at least 14 days before the first dose of alisertib, and the use of these agents is not permitted during the study. 9. Known gastrointestinal (GI) abnormality (including recurrent nausea or vomiting) or GI procedure that could interfere with or modify the oral intake, absorption, or tolerance of alisertib. 10. Participants requiring treatment with clinically significant enzyme inducers, such as the enzyme-inducing antiepileptic drugs phenytoin, carbamazepine, phenobarbital, oxcarbazepine, primidone, rifampin, rifabutin, rifapentine, or St. John's wort within 14 days before the first dose of alisertib or requiring the use of these medications during the study. 11. Requirement for administration of proton pump inhibitor (PPI), H2 antagonist (premedication for paclitaxel allowed), or pancreatic enzymes. Use of any PPI in either continued or intermittent use will be prohibited during the conduct of the study and participants must discontinue any use of PPI within 4 days before the first dose of alisertib. 12. Life-threatening or severe central nervous system (CNS), pulmonary, renal, or hepatic disease unrelated to cancer, or any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. 13. Treatment with any investigational products within 5 half-lives before the first dose of study drug. 14. Treatment with fully human or chimeric monoclonal antibodies within 42 days before the first dose of study drug (21 days if clear evidence of progression). 15. Major surgery within 14 days before the first dose of study drug. 16. Infection requiring systemic intravenous (IV) antibiotic therapy within 14 days preceding the first dose of study drug, or other severe infection. 17. Known human immunodeficiency virus (HIV) positive. 18. Ongoing or active hepatitis B or hepatitis C infection. Testing is not required in the absence of clinical findings or suspicion. 19. History of myocardial infarction, unstable symptomatic ischemic heart disease, uncontrolled hypertension despite appropriate medical therapy, any ongoing cardiac arrhythmias of \> Grade 2, thromboembolic events (eg, deep vein thrombosis, pulmonary embolism, or symptomatic cerebrovascular events), or any other cardiac condition (eg, pericardial effusion or restrictive cardiomyopathy) within 6 months before receiving the first dose of study drug. Chronic stable atrial fibrillation on stable anticoagulant therapy is allowed. Participants with a pacemaker may be enrolled in the study upon discussion with the project clinician. 20. Female participants who are in the lactation period or have a positive serum pregnancy test during the Screening period or a positive urine pregnancy test on Day1 before the first dose of study drug. 21. Diagnosed with or treated for another malignancy within 3 years before the first dose of study drug, or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with non-melanoma skin cancer or carcinoma in situ of any type may be enrolled in the study if they have undergone complete resection and no evidence of active disease is present.