For more information regarding Bristol-Myers Squibb Clinical Trial participation, please visit www.BMSStudyConnect.com Inclusion Criteria: - Fresh pre-treatment and on-treatment tumor biopsy must be provided for biomarker analysis - Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 and at least 1 lesion accessible for biopsy - Eastern Cooperative Oncology Group Performance Status of 0 or 1 - Radiographically documented progressive disease on or after the most recent therapy - Received standard-of-care therapies, including an available programmed death (ligand)-1 inhibitor known to be effective in the tumor type for which they are being evaluated - Parts 1A, 1B, and 2A: Advanced or metastatic non-small cell lung cancer, squamous cell carcinoma of head and neck, microsatellite stable colorectal cancer, gastric/ gastroesophageal junction adenocarcinoma, or cervical cancer, and have received, be refractory to, not be a candidate for, or be intolerant of existing therapies known to provide clinical benefit for the condition of the participant Exclusion Criteria: - Women who are pregnant or breastfeeding - Primary central nervous system (CNS) malignancy - Untreated CNS metastases - Leptomeningeal metastases - Concurrent malignancy requiring treatment or history of prior malignancy active within 2 years prior to the first dose of study treatment - Active, known, or suspected autoimmune disease - Condition requiring systemic treatment with either corticosteroids within 14 days or other immunosuppressive medications within 30 days of the first dose of study treatment - Prior organ or tissue allograft - Uncontrolled or significant cardiovascular disease - Major surgery within 4 weeks of study drug administration - History of or with active interstitial lung disease or pulmonary fibrosis Other protocol-defined inclusion/exclusion criteria apply