Intratumoral/Intralesional Administration of MK-4621/JetPEI™ With or Without Pembrolizumab in Participants With Advanced/Metastatic or Recurrent Solid Tumors (MK-4621-002)

Inclusion Criteria: * Has a histologically- or cytologically-confirmed advanced/metastatic solid tumor by pathology report and has received, or been intolerant to, all treatment known to confer clinical benefit * Has submitted an evaluable baseline tumor sample for analysis before start of treatment * Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale * Demonstrates adequate organ function * Male participants must agree to use approved contraception during the treatment period and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this period * Female participants who are not pregnant or breastfeeding, and who are either not a woman of childbearing potential (WOCBP), or are a WOCBP who agrees to use approved contraception during the treatment period and for at least 120 days after the last dose of study treatment Arms 1 and 2: have 3 lesions defined as follows: 1) at least 1 cutaneous or subcutaneous lesion that is amenable to injection and biopsy (lesion 1) that is measurable as defined by RECIST 1.1, 2) at least 1 discrete non-injected, non-biopsied lesion that is measurable as defined by RECIST 1.1 (lesion 2), and 3) at least 1 discrete and/or distant non-injected lesion amenable for biopsy (lesion 3) Arm 3 only: Has metastatic liver and/or liver lesion involvement that does not exceed one third of the total liver volume in participants to be treated by liver IT injection. Hepatocellular carcinoma participants are excluded from eligibility of intratumoral liver injection. For Arm 3, at least 2 lesions have to be identified as follows: 1) at least 1 liver lesion amenable to image-guided intratumoral injection and biopsy via ultrasound guidance or cross-sectional imaging (CT/MRI) guidance and must be measurable as defined by RECIST 1.1 (lesion 1) and 2) at least 1 other discrete non-injected, non-biopsied lesion that is measurable as defined by RECIST 1.1 (lesion 2) Exclusion Criteria: * Has had chemotherapy, definitive radiation, or biological cancer therapy within 4 weeks prior to the first dose of study therapy, or has not recovered to Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or better from any AEs that were due to cancer therapeutics administered more than 4 weeks earlier * History of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years * Has hepatocellular carcinoma (for Arm 3 only) * Has clinically active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has had a severe hypersensitivity reaction to treatment with a monoclonal antibody/components of the study treatment * Has an active infection requiring therapy * Has history of interstitial lung disease * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis * Has an active autoimmune disease that has required systemic treatment in past 2 years * Has a known history of human immunodeficiency virus (HIV) infection and/or Hepatitis B or C infections, or known to be positive for Hepatitis B surface antigen (HBsAg)/Hepatitis B virus (HBV) DNA or Hepatitis C Antibody or RNA * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorder that would interfere with cooperating with the requirements of the study * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment * Has not fully recovered from any effects of major surgery without significant detectable infection * WOCBP who has a positive urine pregnancy test within 72 hours before the first dose of study treatment * Has received a live-virus vaccine within 30 days of planned treatment start * 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. Prior exposure to immunotherapeutics is allowed, including PD-1 and PD-L1 inhibitors, provided participant did not experience a ≥Grade 3 drug-related toxicity on monotherapy with a PD-1 or PD-L1 inhibitor * Has a history of re-irradiation for squamous cell carcinoma of head and neck (SCCHN) at the projected injection site * Has a tumor(s) in direct contact or encases a major blood vessel and has ulceration and/or fungation onto the skin surface