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