The purpose of this study is to establish the maximum tolerated dose (MTD) and assess the safety and tolerability of MLN4924 (pevonedistat) in combination with docetaxel, paclitaxel and carboplatin, and gemcitabine in participants with solid tumors.

Inclusion Criteria:

1. 18 years of age or older
2. Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1
3. Have a histologically or cytologically confirmed metastatic or locally advanced and incurable solid tumor that is felt to be appropriate for treatment with 1 of the 3 chemotherapy regimens in this study, or have progressed despite standard therapy, or for whom conventional therapy is not considered effective. The tumor must be radiographically or clinically evaluable and/or measurable
4. Recovered (that is, <=Grade 1 toxicity) from the effects of prior antineoplastic therapy
5. Female participants who are post menopausal, surgically sterile, or agree to practice 2 effective methods of contraception or agree to practice true abstinence
6. Male participants who agree to practice effective barrier contraception or agree to practice true abstinence
7. Voluntary written consent must be given before performance of any study-related procedure
8. Suitable venous access for the study-required blood sampling
9. Adequate clinical laboratory values during the screening period as specified in the protocol
10. Participants who are willing to refrain from donating blood for at least 90 days after their final dose of MLN4924 and (for male participants) willing to refrain from donating semen for at least 4 months after their final dose of MLN4924
11. Availability of fixed tumor specimen (block or slides) for exploratory biomarker analysis. If no slides or block are available, fresh tumor biopsies should be obtained and used for these assessments

Exclusion Criteria:

1. Major surgery within 14 days before the first dose of study drug
2. Female participants who are lactating or pregnant
3. Active uncontrolled infection or severe infectious disease
4. Receiving antibiotic therapy within 14 days before the first dose of study treatment
5. Life-threatening illness unrelated to cancer
6. Known hypersensitivity to study-assigned chemotherapy
7. Prior treatment with MLN4924; however, prior treatment with docetaxel, paclitaxel,carboplatin, and gemcitabine is allowed
8. History of severe hypersensitivity reactions to docetaxel (polysorbate 80-based formulations) for participants to be enrolled in Arm 1 (MLN4924 + docetaxel), history of hypersensitivity to carboplatin for participants to be enrolled in Arm 2 (MLN4924 + paclitaxel + carboplatin), or history of severe hypersensitivity to paclitaxel (cremophor-based formulations) for participants to be enrolled in Arm 2
9. Persistent diarrhea (greater than Grade 2) lasting >3 days within 2 weeks before the first dose of study treatment
10. Systemic antineoplastic therapy within 21 days before the first dose of study drug
11. Radiotherapy within 14 days preceding the first dose of study treatment
12. Prior treatment with radiation therapy involving greater than or equal to (>=) 25% of the hematopoietically active bone marrow
13. Treatment with cytochrome P450 3A (CYP3A) inducers within 14 days before the first dose of MLN4924.

Treatment with CYP3A inhibitors within 14 days before the first dose of MLN4924; however, voriconazole and fluconazole need only be stopped for 3 days before MLN4924. Participants must have no history of amiodarone use in the 6 months before the first dose of MLN4924 14. Clinically uncontrolled central nervous system (CNS) involvement 15. Any serious medical or psychiatric illness 16. Treatment with any investigational products 21 days prior to treatment 17. Unwilling or unable to refrain from using statins 24 hours before, the day of, and 24 hours after each MLN4924 administration 18. Known human immunodeficiency virus (HIV) positive or hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection 19. Known hepatic cirrhosis 20. Known cardiac/cardiopulmonary disease 21. Left ventricular ejection fraction 23. with a cardiac pacer whose heart rate is set at a fixed rate and participants on concomitant medication that may limit increase in heart rate in response to hypotension 24 History of severe intolerance to cytotoxic agent(s) given in the assigned arm

Takeda makes patient-level, de-identified data sets and associated documents available for all interventional studies after applicable marketing approvals and commercial availability have been received (or program is completely terminated), an opportunity for the primary publication of the research and final report development has been allowed, and other criteria have been met as set forth in Takeda's Data Sharing Policy (see www.TakedaClinicalTrials.com for details). To obtain access, researchers must submit a legitimate academic research proposal for adjudication by an independent review panel, who will review the scientific merit of the research and the requestor's qualifications and conflict of interest that can result in potential bias. Once approved, qualified researchers who sign a data sharing agreement are provided access to these data in a secure research environment.