Inclusion criteria - In Part A: Histological or cytological diagnosis of MEL or any type of carcinoma, progressive metastatic disease, or progressive locally advanced disease not amenable to local therapy. In Part B of the study, only histological diagnoses of metastatic MEL with progressively locally advanced or metastatic disease are eligible for participation. - Failure of established standard medical anti-cancer therapies for a given tumor type or intolerance to such therapy. - In Part B of the study, MEL must be measurable by imaging. - Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale. - Adequate organ function. Exclusion criteria - Chemotherapy, radioactive, or biological cancer therapy within 4 weeks prior to the first dose of study therapy, or not recovered to Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or better from the adverse events caused by therapy administered more than 4 weeks prior to first dose. - Participation in a study of an investigational agent or using an investigational device within 30 days of administration of MK-3475. - Other form(s) of antineoplastic therapy anticipated during the period of the study. - Chronic systemic steroid therapy, or on any other form of immunosuppressive medication. - Chronic anti-coagulation treatment with warfarin. - History of a hematologic malignancy, primary brain tumor, sarcoma, or another primary solid tumor, unless no evidence of that disease for 5 years. - Active central nervous system (CNS) metastases and/or carcinomatous meningitis. - Previous severe hypersensitivity reaction to another monoclonal antibody (mAb). - Active autoimmune disease or a documented history of autoimmune disease, except vitiligo or resolved childhood asthma/atopy. - Prior therapy with an anti-programmed cell death (PD)-1 or an antibody targeting other immuno-regulatory receptors or mechanisms (with exception of ipilimumab in study Part B). - Active infection requiring therapy. - Positive for Human Immunodeficiency Virus (HIV), Hepatitis B (Hepatitis B Surface Antigen [HBsAg] reactive), or Hepatitis C virus (Hepatitis C Virus Ribonucleic Acid [HCV RNA] (qualitative) is detected). - Regular use of illicit drugs or a recent history (within the last year) of substance abuse (including alcohol). - Symptomatic ascites or pleural effusion. - Participant is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study.