Study of MK-4166 and MK-4166 in Combination With Pembrolizumab (MK-3475) in Participants With Advanced Solid Tumors (MK-4166-001)

Inclusion criteria:

* Has a histologically- or cytologically-confirmed metastatic solid tumor for which there is no available therapy which may convey clinical benefit. Part E: Has advanced malignant melanoma.
* Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1
* Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale
* Adequate organ function
* Female participants of childbearing potential must have a negative urine or serum pregnancy test and must be surgically sterile or willing to use 2 methods of birth control or abstain from heterosexual activity for the course of the study through 120 days after last dose of study drug
* Male participants must agree to use an adequate method of contraception during sexual contact with females of childbearing potential starting with the first dose of study drug through 180 days after the last dose of study drug
* Submit an evaluable tumor sample for analysis.

Exclusion criteria:

* Chemotherapy, radiation, or biological cancer therapy within 4 weeks prior to the first dose of study drug, or who has not recovered to Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or better from the adverse events due to cancer therapeutics administered more than 4 weeks earlier
* Currently participating or has participated in a study of an investigational agent or using an investigational device within 28 days of administration of MK-4166
* Expected to require any other form of antineoplastic therapy while on study
* On chronic systemic steroid therapy in excess of replacement doses, or on any other form of immunosuppressive medication
* History of a malignancy for which potentially curative treatment has been completed, with no evidence of malignancy for 5 years excepting successful definitive resection of basal cell carcinoma of the skin, superficial bladder cancer, or in situ cervical cancer
* Known active central nervous system (CNS) metastases and/or carcinomatous meningitis
* Severe hypersensitivity reaction to treatment with another monoclonal antibody
* Active autoimmune disease or a documented history of autoimmune disease, except vitiligo or resolved childhood asthma/atopy
* Active infection requiring therapy
* Current pneumonitis, or a history of (non-infectious) pneumonitis that required steroids
* Prior stem cell or bone marrow transplant
* Positive for human immunodeficiency virus (HIV), Hepatitis B, or Hepatitis C
* Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Regular user (including "recreational use") of any illicit drugs or recent history (within the last year) of substance abuse (including alcohol)
* Symptomatic ascites or pleural effusion
* Pregnant, breastfeeding, or expecting to conceive or father children within the projected duration of the study
* Clinically significant heart disease
* Major surgery in the past 16 weeks
* Received a live vaccine within 30 days prior to first dose of study drug