Study of MK-8353 + Selumetinib in Advanced/Metastatic Solid Tumors (MK-8353-014)

Inclusion Criteria:

* Have a histologically- or cytologically-documented, locally-advanced or metastatic solid tumor by pathology report and have received, or been intolerant to, all treatment known to confer clinical benefit.
* Provide an archival or newly obtained tumor tissue sample and blood samples for assessment of proto-oncogene rat sarcoma virus (RAS)/rapidly accelerated fibrosarcoma (RAF) mutation and for biomarker analysis.
* Have at least 1 measurable lesion as defined by Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) on imaging studies (computed tomography \[CT\] or magnetic resonance imaging \[MRI\]) as assessed by the investigator/local radiology review.
* Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale. (Obtain within 7 days prior to first dose of study treatment.)
* Have the ability to swallow and retain oral medication.
* Demonstrate adequate organ function.
* Male participants must agree to use an acceptable 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.
* Female participants must not be pregnant, not breastfeeding, and either not a woman of childbearing potential (WOCBP) or a WOCBP who agrees to follow the study's contraceptive guidance during the treatment period and for at least 120 days, after the last dose of study intervention.

Exclusion Criteria:

* Have 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 National Cancer Institute 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 (this includes participants with previous immunomodulatory therapy with residual immune-related AEs).
* Have clinically active central nervous system metastases and/or carcinomatous meningitis.
* Have an active infection requiring therapy.
* Have known human immunodeficiency virus (HIV) and/or Hepatitis B or C infections, or known to be positive for Hepatitis B antigen (HBsAg)/ Hepatitis B virus (HBV) deoxyribonucleic acid (DNA) or Hepatitis C Antibody or ribonucleic acid (RNA).
* Have clinically significant cardiovascular disease as defined by study criteria.
* Have a history of thromboembolic or cerebrovascular events within 6 months prior to treatment start, including transient ischemic attacks (TIAs), cerebrovascular accidents (CVAs), deep vein thrombosis, or pulmonary embolism.
* Have neuromuscular disorders associated with an elevated creatine kinase (e.g., inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy).
* Have one or more study-defined ophthalmological findings/conditions.
* Have a known history of Gilbert's Syndrome.
* Have a history or current evidence of a gastrointestinal (GI) condition (e.g., inflammatory bowel disease, Crohn's disease, ulcerative colitis) or impaired liver function or diseases that in the opinion of the investigator may significantly alter the absorption or metabolism of oral medications.
* Have a known psychiatric or substance abuse disorder, or any other cognitive 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, starting with the Screening Visit through 120 days after the last dose of study treatment.
* Received prior therapy with a mitogen activated protein kinase (MEK) inhibitor (e.g., cobimetinib, trametinib), or an extracellular signal-regulated kinase (ERK) inhibitor (e.g., MK-8353, GCD-0994, ulixertinib), or a proto-oncogene BRAF inhibitor (e.g., dabrafenib, vemurafenib).
* 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.
* Have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to agents and/or excipients used in the study.
* A WOCBP who has a positive urine pregnancy test within 24 hours before the first dose of study treatment