• Number of Participants Experiencing Dose-Limiting Toxicities (DLTs) [ Time Frame: Up to Day 21 of Cycle 1 (each cycle is 21 days) ]
  DLTs are defined as toxicities that: 1) are possibly, probably, or definitely related to study therapy; and 2) meet pre-defined severity criteria. For each arm, the number of participants experiencing DLTs will be assessed.
• Number of Participants Experiencing an Adverse Event (AE) [ Time Frame: Up to 40 months ]
  An AE is any unfavorable and unintended sign, symptom, or disease (new or exacerbated) in a clinical study participant, temporally associated with the use of study treatment, whether or not considered related to the study treatment. For each arm, the number of participants experiencing an AE will be assessed.
• Number of Participants Discontinuing Study Treatment due to an Adverse Event [ Time Frame: Up to 27 months ]
  An AE is any unfavorable and unintended sign, symptom, or disease (new or exacerbated) in a clinical study participant, temporally associated with the use of study treatment, whether or not considered related to the study treatment. For each arm, the number of participants discontinuing study treatment due to an AE will be assessed.

• Area Under the Concentration-Time Curve (AUC) of Selumetinib [ Time Frame: [Cycle 1]: At designated time points; up to 3 weeks (each cycle is 21 days) ]
  Plasma selumetinib concentration will be quantified for each arm to determine AUC, defined as the area under the concentration-time curve for selumetinib.
• Maximum Observed Plasma Concentration (Cmax) of Selumetinib [ Time Frame: [Cycle 1]: At designated time points; up to 3 weeks (each cycle is 21 days) ]
  Plasma selumetinib concentration will be quantified for each arm to determine Cmax, defined as the maximum observed concentration of selumetinib in plasma.
• Minimum Observed Plasma Concentration (Cmin) of Selumetinib [ Time Frame: [Cycles 1 to 5]: At designated time points; up to 15 weeks (each cycle is 21 days) ]
  Plasma selumetinib concentration will be quantified for each arm to determine Cmin, defined as the minimum observed concentration of selumetinib in plasma.

• Drug: Selumetinib
  Selumetinib oral capsules administered BID at escalating dose levels. Selumetinib administered only in weeks 1&2 of each 3-week treatment cycle.
  Other Name: MK-5618
• Biological: Pembrolizumab
  Pembrolizumab administered by IV infusion at 200 mg Q3W, given on cycle day 1 of each 3-week treatment cycle.
  Other Names:

  • KEYTRUDA®
  • MK-3475

• Experimental: Selumetinib at Dose Level 1 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; every three weeks [Q3W]) in combination with selumetinib at dose level 1 (dosed orally; twice daily [BID]) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab
• Experimental: Selumetinib at Dose Level 2 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; Q3W) in combination with selumetinib at dose level 2 (dosed orally; BID) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab
• Experimental: Selumetinib at Dose Level 3 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; Q3W) in combination with selumetinib at dose level 3 (dosed orally; BID) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab
• Experimental: Selumetinib at Dose Level 4 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; Q3W) in combination with selumetinib at dose level 4 (dosed orally; BID) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab
• Experimental: Selumetinib at Dose Level 5 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; Q3W) in combination with selumetinib at dose level 5 (dosed orally; BID) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab
• Experimental: Selumetinib at Dose Level 6 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; Q3W) in combination with selumetinib at dose level 6 (dosed orally; BID) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab
• Experimental: Selumetinib at Dose Level 7 + Pembrolizumab
  Participants receive 200 mg pembrolizumab (IV infusion; Q3W) in combination with selumetinib at dose level 7 (dosed orally; BID) for up to 35 treatment cycles (cycle length: 3 weeks). During each 3-week cycle, selumetinib will be administered only for the first two weeks.
  Interventions:

  • Drug: Selumetinib
  • Biological: Pembrolizumab

Inclusion Criteria:

• Has a histologically or cytologically confirmed advanced or metastatic solid tumor by pathology report and have received, or been intolerant to, all treatment known to confer clinical benefit.
• Has measurable disease by Response Evaluation Criteria in Solid Tumors, Version 1.1 (RECIST 1.1) as assessed by local site investigator/radiology. Target lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions.
• Has a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale.
• Is able to swallow and retain oral medication and has no clinically significant gastrointestinal abnormalities that might alter absorption.
• Has adequate organ function.
• If male, agree to use a contraception during the treatment period and for at least 120 days after the last dose of study intervention and refrain from donating sperm during this period.
• If female, is not pregnant or breastfeeding, and is not a woman of childbearing potential (WOCBP). If a WOCBP, agree to follow the contraceptive guidance during the treatment period and for at least 120 days after the last dose of study intervention.
• For Human immunodeficiency virus (HIV) infected participants, must have well controlled HIV on a stable regimen of anti-retroviral therapy (ART). Participants on ART must have been without changes in drugs or dose modification for at least 4 weeks prior to study entry.

Exclusion Criteria:

• Has had chemotherapy, definitive radiation, or biological cancer therapy within 4 weeks (2 weeks for palliative radiation) prior to the first dose of study treatment, or has not recovered to Common Toxicity Criteria for Adverse Events (CTCAE) Grade 1 or better from any AEs that were due to cancer therapeutics administered more than 4 weeks earlier (this includes participants with previous immunomodulatory therapy with residual immune-related AEs). Participants receiving ongoing replacement hormone therapy for endocrine immune-related AEs will not be excluded from participation in this study.
• Has clinically active central nervous system metastases and/or carcinomatous meningitis.
• Has had a severe hypersensitivity reaction (≥ Grade 3) to treatment with a monoclonal antibody/component of the study treatment, and/or has a history of allergic reactions attributed to compounds of similar chemical or biologic composition to agents and/or excipients used in the study.
• Has an active infection requiring therapy.
• 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 the past 2 years except vitiligo or resolved childhood asthma/atopy. Replacement therapy, such as thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, is not considered a form of systemic treatment and is allowed. Use of non-systemic steroids is permitted.
• Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to allocation.
• Has known Hepatitis B or C infection.
• For HIV infected participants, has a history of Kaposi's sarcoma and/or Multicentric Castleman's Disease.
• Has undergone major surgery and has not recovered adequately from any toxicity and/or complications from the intervention prior to starting study therapy.
• Has baseline peripheral neuropathy/paresthesia Grade 1.
• Has any medical, psychiatric, cognitive, or other condition that may compromise the participant's ability to understand the participant information, give informed consent, comply with the study protocol, or complete the study, in the opinion of the treating investigator.
• Participants with clinically significant cardiovascular disease as defined by the following: 1) Uncontrolled hypertension; 2) Left ventricular ejection fraction (LVEF) <55%; 3) Symptomatic heart failure (New York Heart Association (NYHA) Grade II to IV), prior or current cardiomyopathy, or severe valvular heart disease; 4) Uncontrolled angina; 5) Clinically significant cardiac arrhythmia and/or conduction abnormality ≤6 months prior to start of study treatment; 6) Myocardial infarction or acute coronary syndrome ≤6 months prior to start of study treatment; 7) Mean QT interval calculated according to the Frederica method (QTcF) interval: Male >450 ms; Female >470 ms.
• Has a history of thromboembolic or cerebrovascular event(s) within 6 months prior to study enrollment, including transient ischemic attack, cerebrovascular accident, deep vein thrombosis, or pulmonary embolism.
• Has a neuromuscular disorder associated with an elevated creatine kinase (e.g., inflammatory myopathy, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy.
• Has a history of, or current, retinal vein occlusion (RVO) or current risk factors for RVO (e.g., uncontrolled glaucoma, ocular hypertension, history of hyperviscosity, or hypercoagulability syndromes).
• Has retinal degenerative disease.
• 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, make administration of the study treatments hazardous or make it difficult to monitor adverse effects such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator.
• Has a known psychiatric or substance abuse disorder that would interfere with the Participant's ability to cooperate with the requirements of the study.
• Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study.
• Has received a live-virus vaccine within 28 days of planned treatment start. Seasonal flu vaccines that do not contain live virus are permitted.
• Is currently participating and receiving study treatment in a study of an investigational agent or has participated and received study treatment in a study of an investigational agent or has used an investigational device within 28 days of administration of selumetinib.
• Is a WOCBP who has a positive urine pregnancy test within 24 hours before the first dose of study treatment.