Study of Vibostolimab Alone and in Combination With Pembrolizumab in Advanced Solid Tumors (MK-7684-001) ( KEYVIBE-001)

Inclusion Criteria:

* For Part A participants enrolled prior to Amendment 7, must have a histologically or cytologically confirmed metastatic solid tumor for which there is no available therapy that is expected to convey clinical benefit
* For Part A Japanese cohort added with Amendment 7: Must reside in Japan and be of Japanese descent and have adenocarcinoma of the stomach and/or gastric-esophageal junction (GEJ) that is considered inoperable and that has received, and progressed on, at least 1 prior chemotherapy regimen or human epidermal growth factor receptor 2 (HER2)/neu-targeted approved therapy (if HER2/neu-positive). In both cases, participants may be untreated or could have received and progressed on 1 prior regimen, but must not have received prior anti-PD-1/PD-L1 therapy
* For Part A participants with non-small cell lung cancer (NSCLC) added with Amendment 7: Must have a histologically or cytologically confirmed diagnosis of stage IV (M1a or M1b per current American Joint Committee on Cancer criteria, edition 8) non-squamous NSCLC
* For Part B China participants added with Amendment 12. Must have a histologically or cytologically confirmed metastatic solid tumor for which no more than 2 prior lines of therapy were administered and there is no available therapy that is expected to convey clinical benefit AND be Chinese from mainland China
* For Parts A and B: Has histologically or cytologically confirmed metastatic solid tumor
* Has measurable disease by Response Evaluation Criteria In Solid Tumors (RECIST)
* Has an Eastern Cooperative Oncology Group performance status of 0 to 1
* Females must not be pregnant
* Women of childbearing potential and male participants must agree to use adequate contraception for the course of the study
* Has provided a tumor tissue sample (archival or newly obtained core or excisional biopsy of a tumor lesion)
* For Chinese participants enrolled as part of Amendment 12. No tumor tissue samples will be collected

Exclusion Criteria:

* Has had chemotherapy, radiation, biological cancer therapy or major surgery within 4 weeks prior to the first dose of study treatment
* Has not recovered to Common Toxicity Criteria for Adverse Events Grade 1 or better from the adverse events due to cancer therapeutics administered more than 4 weeks prior to the first dose of study treatment
* Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment
* Has received previous treatment with another agent targeting the T cell immunoglobulin and immunoreceptor tyrosine-based inhibitory motif (TIGIT) receptor
* Has received previous treatment with an immunomodulatory agent (e.g., anti-programmed cell death 1, anti-programmed cell death ligand 1 or cytotoxic T-lymphocyte-associated protein 4) and was discontinued from that treatment due to a Grade 3 or higher immune-related adverse event
* Is expected to require any other form of antineoplastic therapy while participating in the trial
* Is on chronic systemic steroid therapy in excess of replacement doses or on any other form of immunosuppressive medication
* Has a history of a previous additional malignancy unless potentially curative treatment has been completed with no evidence of malignancy for 5 years
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis
* Has an active autoimmune disease
* Has an active infection requiring systemic treatment
* Has interstitial lung disease
* Has active or past history of (non-infectious) pneumonitis requiring steroids
* Has symptomatic ascites or pleural effusion
* Has previously had a hematopoetic stem cell transplant or solid organ transplant
* Is known to be human immunodeficiency virus (HIV) positive and/or known to have active chronic or acute Hepatitis B or Hepatitis C
* Has a known psychiatric and/or substance abuse disorder that would make it difficult for the participant to cooperate with the requirements of the trial
* Is a regular user (including recreational use) of any illicit drugs at the time of providing documented informed consent, or has a recent history (within the last year) of substance abuse
* Has received a live virus vaccine within 30 days prior to the first dose of study treatment
* Has had hormonal cancer therapy (e.g., tamoxifen, leuprolide). within 4 weeks prior to the first dose of study treatment
* For Part A participants with NSCLC added with Amendment 7: Is unable to interrupt aspirin or other nonsteroidal anti-inflammatory drugs (NSAIDs) other than an aspirin dose ≤1.3 gram per day for a 5-day period (8-day period for long-acting agents, such as piroxicam)
* For Part A participants with NSCLC added with Amendment 7: Is unable or unwilling to take folic acid or Vitamin B12 supplementation