Study of MLN2480 in Participants With Relapsed or Refractory Solid Tumors Followed by a Dose Expansion in Participants With Metastatic Melanoma

Inclusion Criteria:

1. Informed consent.
2. Male or female participants 18 years or older.
3. Dose Escalation phase: Participants with solid tumors (including melanoma) who have failed or are not candidates for standard therapies of for whom no approved therapy is available.
4. Dose Expansion phase: Metastatic melanoma (locally advanced or metastatic melanoma).
5. Dose Expansion phase: At least 1 measurable lesion which has not been treated previously with radiotherapy. A newly arising lesion in a previously irradiated field is acceptable.
6. For participants undergoing biopsy procedures: Prothrombin time (PT) and activated partial thromboplastin time (aPTT) must be within the normal range.
7. Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to (\<=) 1.
8. Adequate tissue sample from either archival formalin-fixed paraffin-embedded (FFPE) tumor tissue or new biopsy of tumor.
9. Previous chemotherapy, immunotherapy, and hormone therapy must be completed at least 4 weeks prior to the administration of MLN2480 and radiation must be completed at least 3 weeks prior to the administration of MLN2480; all associated toxicity must be resolved to \<=Grade 1.
10. Expected survival time of at least 3 months in the opinion of the investigator.
11. Participants who do not have hypo- or hyperthyroidism.
12. Ability to swallow and retain oral medication.
13. Female participants who are postmenopausal for at least 1 year, surgically sterile, or agree to practice 2 effective methods of contraception through 3 months after the last dose of study drug or agree to practice true abstinence.
14. Male participants who, even if surgically sterilized, agree to practice effective barrier contraception through 3 months after the last dose of alisertib or agree to practice true abstinence.

Exclusion Criteria

1. History of any major disease that might interfere with safe protocol participation.
2. Dose Expansion phase: Previous treatment with RAF or MEK inhibitors.
3. Laboratory values as specified in study protocol.
4. Current enrollment in any other investigational treatment study.
5. Evidence of current uncontrolled cardiovascular conditions within the past 6 months.
6. Prior investigational agents for malignant or non-malignant disease within 4 weeks prior to Day 1.
7. Active hepatitis or human immunodeficiency virus (HIV) infection.
8. Active bacterial or viral infection.
9. Female participants who are pregnant or currently breastfeeding.
10. Major surgery within 28 days of Day 1.
11. Refractory nausea and vomiting, malabsorption, or significant bowel or stomach resection.
12. Inability to comply with study requirements.
13. Other unspecified reasons that, in the opinion of the investigator or Millennium, make the participant unsuitable for enrollment.