Safety and Efficacy of Pembrolizumab (MK-3475) Plus Binimetinib Alone or Pembrolizumab Plus Chemotherapy With or Without Binimetinib in Metastatic Colorectal Cancer (mCRC) Participants (MK-3475-651/KEYNOTE-651)

Inclusion Criteria:

* At least 18 years of age
* Has a histologically-confirmed, unresectable or metastatic (Stage IV American Joint Committee on Cancer \[AJCC seventh edition\]) colorectal cancer (CRC)
* Has a locally determined non microsatellite instability high/ proficient mismatch repair (non-MSI-H/pMMR) tumor status
* Has at least 1 radiologically measurable lesion as defined by RECIST 1.1
* Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Has a life expectancy of at least 3 months
* Has the ability to swallow and retain oral medication and not have any clinically significant gastrointestinal abnormalities that might alter absorption.
* Has adequate organ function
* Male participants must agree to use contraception during the treatment period and for ≥180 days, after the last dose of study treatment and refrain from donating sperm during this period. Male participants with pregnant partners must agree to use a condom
* Female participants eligible to participate if not pregnant, not breastfeeding, and is not a woman of childbearing potential (WOCBP) or is a WOCBP who agrees to follow contraceptive guidance during the treatment period and for ≥180 days after the last dose of study treatment

  * Participants for Cohort A:
* Has been previously treated with fluoropyrimidine, irinotecan, and oxaliplatin

  * Participants for Cohorts B and C:
* Must not have received prior systemic chemotherapy for Stage IV CRC

  * Participants for Cohorts D and E:
* Must have been previously treated with 1 line of therapy including a fluoropyrimidine plus an oxaliplatin-based regimen

  * Participants for Cohorts A, C, and E:
* Have a 12-lead electrocardiogram (ECG) and echocardiogram (ECHO) or multigated acquisition (MUGA) scan performed by the investigator or other qualified person to evaluate cardiac function prior to enrollment in the study

Exclusion Criteria:

* Is currently participating and receiving study therapy in a study of an investigational agent or has participated and received study therapy in a study of an investigational agent or has used an investigational device within 28 days of administration of MK-3475
* 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) Gr 1 or better from any AEs that were due to cancer therapeutics administered more than 4 weeks earlier
* Has history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years
* Has clinically active central nervous system (CNS) metastases and/or carcinomatous meningitis
* Has a known hypersensitivity, intolerability or contraindication to any component of study treatment, including premedication
* Has any active infection requiring systemic therapy
* Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis
* Has received prior therapy with compounds targeting programmed death (PD)-1, PD-L1, PD-L2, or a mitogen-activated protein kinase (MAPK) pathway inhibitor
* Has an autoimmune disease that has required systemic treatment in the past 2 years with use of disease modifying agents, corticosteroids, or immunosuppressive drugs
* Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to randomization
* Has known history of human immunodeficiency virus (HIV) infection
* Has a known history of Hepatitis B
* Has received live vaccine within 30 days of the planned start of study therapy
* 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
* Has any medical, psychiatric, cognitive, or other conditions that may compromise the participant's ability to understand the participant information, give informed consent, comply with the study protocol, or complete the study.
* Has symptomatic congestive heart failure (CHF)
* Has a history of acute or chronic pancreatitis
* Has existing uncontrolled arterial hypertension (systolic blood pressure \[SBP\] ≥150 mmHg or diastolic blood pressure \[DBP\] ≥100 mmHg) despite appropriate medical therapy
* Has a history of thromboembolic or cerebrovascular events within 6 months prior to registration
* Has neuromuscular disorders associated with an elevated creatine kinase
* A WOCBP who has a positive urine pregnancy test within 24 hours before the first dose of study treatment

  * Potential Participants for Cohorts A, C or E who are to Receive Binimetinib:
* Has a history of, or current, retinal vein occlusion (RVO) or current risk factors for RVO
* Has retinal degenerative disease

  * Potential Participants for Cohorts A, C, D or E:
* Has a known history of Gilbert's Syndrome

  * Potential Participants for Cohorts D or E:
* Has a previous treatment with irinotecan
* Has plans to use, or is using, any herbal medications/supplements or any medications or foods that are strong inhibitors or inducers of cytochrome P450 3A 4/5 ≤1 week prior to the start of study treatment