Study to Evaluate the Safety, Tolerability, and Pharmacodynamics of Investigational Treatments in Combination With Standard of Care Immune Checkpoint Inhibitors in Participants With Advanced Melanoma

You may be eligible if

• 1. Is a male or female participant of 18 years or older.
• 2. Has histologically confirmed, unresectable Stage III or Stage IV melanoma per the American Joint Committee on Cancer (AJCC) staging system.
• 3. Has an eastern cooperative oncology group (ECOG) performance status of 0-1.
• 4. Adequate bone marrow reserve and renal and hepatic function within 28 days before the first dose of study drug on the basis of the defined laboratory parameters.
• 5. For TAK-580 + nivolumab and TAK-202 (plozalizumab) + nivolumab only: Had disease accessible for repeat nonsignificant risk biopsy (those occurring outside the brain, lung/mediastinum, and pancreas, or obtained with endoscopic procedures extending beyond the esophagus, stomach, or bowel) and willingness to undergo serial tumor biopsies.
• 6. Additional Inclusion Requirements for TAK-580 + nivolumab
• a) BRAF V600 mutation-positive or NRAS mutation-positive disease previously untreated with RAF, MEK, or other inhibitors of the mitogen-activated protein kinase (MAPK) pathway. Participants who have progressed on these agents can still be enrolled in TAK-202 (plozalizumab) + nivolumab or vedolizumab + nivolumab + ipilimumab.
• 7. Additional Inclusion Requirements for expansion cohorts only a) Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) guidelines (Version 1.1) and at least 1 nonsignificant risk, non-target lesion accessible for biopsy per the guidelines above (for TAK-580 + nivolumab and TAK-202 (plozalizumab) + nivolumab only).
• 2. Completed a prior therapy less than (\<) 2 weeks prior to first dose and for whom adverse events (AEs) related to prior therapy had not returned to baseline or improved to Grade 1.
• 3. Has active, known or suspected autoimmune disease.
• 4. Has a condition requiring systemic treatment with either corticosteroids or other immunosuppressive medications within 14 days of study drug administration.
• 5. Has a history of pneumonitis requiring treatment with steroids; history of idiopathic pulmonary fibrosis (including pneumonitis), interstitial lung disease, drug-induced pneumonitis, organizing pneumonia, or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted.
• 6. Is previously diagnosed human immunodeficiency virus (HIV) infection or active hepatitis B or C.
• 7. Additional Exclusion Requirements for arm 1 only (nivolumab Plus TAK-580)
• 1. Concomitant use or administration of clinically significant enzyme inducers less than or equal to (\<=) 14 days before the first dose of TAK-580.
• 2. Treatment with gemfibrozil (or other strong CYP2C8 inhibitor) within 14 days before the first dose of TAK-580.
• 3. Left ventricular ejection fraction (LVEF) \<50 percent (%) as measured by echocardiogram (ECHO) or multiple gated acquisition scan (MUGA) within 4 weeks before receiving the first dose of study drug.
• 4. Known gastrointestinal (GI) disease or prior GI procedure that could interfere with the oral absorption or tolerance of the TAK-580.
• 8. Additional Exclusion Requirements for arm 3 only (vedolizumab Plus nivolumab Plus ipilimumab)
• 1. Had prior exposure to rituximab, natalizumab, vedolizumab, or alemtuzumab.
• 2. Has a history of any major neurological disorders, including stroke, multiple sclerosis, or neurodegenerative disease.
• 3. Has taken any live vaccinations within 30 days before study drug administration except for the influenza vaccine.