Inclusion Criteria:

          -  Has histologically or cytologically confirmed diagnosis of unresectable and metastatic
             colorectal adenocarcinoma (Stage IV A, B and C as defined by American Joint Committee
             on Cancer [AJCC] 8th edition). Note: Tumor must be determined to be NOT microsatellite
             instability-high (MSI-H)/mismatch repair deficient (dMMR) by local testing

          -  Has been previously treated for their disease and has shown disease progression as
             defined by RECIST 1.1 on or after or could not tolerate standard treatment, which must
             include ALL of the following agents if approved and locally available in the country
             where the participant is randomized:

               1. fluoropyrimidine, irinotecan and oxaliplatin

               2. with or without an anti-vascular endothelial growth factor (VEGF) monoclonal
                  antibody (bevacizumab)

               3. with anti- epidermal growth factor receptor (EGFR) monoclonal antibodies
                  (cetuximab or panitumumab) for RAS (KRAS/NRAS) wild-type (WT) participants

               4. BRAF inhibitor (in combination with cetuximab +/- binimetinib) for BRAF V600E
                  mutated metastatic colon cancer (mCRC)

          -  Has measurable disease per RECIST 1.1 assessed by the investigator

          -  Has provided to a designated central laboratory an archival tumor tissue sample or
             newly obtained core, incisional, or excisional biopsy of a tumor lesion which has not
             been previously irradiated

          -  Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 within 3
             days prior to randomization

          -  Has a life expectancy of at least 3 months, based on the investigator assessment

          -  Has the ability to swallow capsules or ingest a suspension orally or by a feeding tube

          -  Has adequately controlled blood pressure (BP) with or without antihypertensive
             medications, defined as BP ≤150/90 millimeter of mercury (mmHg) with no change in
             antihypertensive medications within 1 week prior to randomization

          -  Male participants must agree to the following during the treatment period and for at
             least 90 days after the last dose of regorafenib or TAS-102 and at least 7 days after
             the last dose of lenvatinib: refrain from donating sperm PLUS either be abstinent from
             heterosexual intercourse as their preferred and usual lifestyle or use contraception.
             The male contraception period should continue for at least 7 days after
             discontinuation of lenvatinib

          -  A female participant is eligible to participate if she is not pregnant or
             breastfeeding, and at least one of the following conditions applies: is not a woman of
             childbearing potential (WOCBP) OR is a WOCBP and using a highly-effective
             contraceptive method during the treatment period and for at least 30 days after the
             last dose of lenvatinib, 120 days after the last dose of pembrolizumab, and 180 days
             after the last dose of regorafenib or TAS-102 (whichever is last) AND agrees not to
             donate eggs (ova, oocytes)

          -  A WOCBP must have a negative highly sensitive pregnancy test (urine or serum) within
             24 hours before the first dose of study treatment

        Exclusion Criteria:

          -  Has a tumor that is microsatellite instability-high (MSI-H)/mismatch repair deficient
             (dMMR) per local testing

          -  Has presence of gastrointestinal condition, eg, malabsorption, that might affect the
             absorption of study drug.

          -  Has present or progressive accumulation of pleural, ascitic, or pericardial fluid
             requiring drainage or diuretic drugs within 2 weeks prior to enrollment

          -  Has radiographic evidence of encasement or invasion of a major blood vessel invasion
             or of intratumoral cavitation. In the chest, major blood vessels include the main
             pulmonary artery, the left and right pulmonary arteries, the 4 major pulmonary veins,
             the superior or inferior vena cava, and the aorta

          -  Has clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the
             first dose of study drug

          -  Has clinically significant cardiovascular disease within 12 months from first dose of
             study intervention, including New York Heart Association Class III or IV congestive
             heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or
             cardiac arrhythmia associated with hemodynamic instability.

        Participants with cardiac failure NYHA Class II, III and IV are not allowed to be assigned
        to the regorafenib in Arm B

          -  Has a history of arterial thromboembolism within 12 months of start of study drug

          -  Has urine protein ≥1 gram/24 hour

          -  Has prolongation of QT interval corrected with Fridericia's formula (QTcF interval) to
             >480 milliseconds

          -  Has left ventricular ejection fraction (LVEF) below the institutional (or local
             laboratory) normal range as determined by multigated acquisition (MUGA) or
             echocardiogram (ECHO)

          -  Has a known additional malignancy that is progressing or has required active treatment
             within the past 3 years with certain exceptions

          -  Has serious nonhealing wound, ulcer or bone fracture

          -  Has had major surgery within 3 weeks prior to first dose of study treatment

          -  Has received biologic response modifiers (eg, granulocyte colony-stimulating factor)
             within 4 weeks before study entry

          -  Has preexisting ≥Grade 3 gastrointestinal or nongastrointestinal fistula

          -  Has received prior treatment with a combination of an anti-PD-1, anti-PD-L1, or anti
             PD-L2 agent with anti-VEGF monoclonal antibodies or vascular endothelial growth factor
             receptor (VEGFR) inhibitors

          -  Has previously received regorafenib or TAS-102

          -  Has received prior systemic anti-cancer therapy including investigational agents
             within 28 days prior to randomization

          -  Has received prior radiotherapy within 2 weeks of start of study treatment

          -  Has received a live or live-attenuated vaccine within 30 days prior to the first dose
             of study treatment

          -  Has known intolerance to lenvatinib, regorafenib, or TAS-102 and/or any of their
             excipients

          -  Is currently participating in or has participated in a study of an investigational
             agent or has used an investigational device within 28 days prior to the first dose of
             study treatment

          -  Has known central nervous system (CNS) metastases and/or carcinomatous meningitis.

          -  Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients

          -  Has an active autoimmune disease that has required systemic treatment in past 2 years

          -  Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy
             (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of
             immunosuppressive therapy within 7 days prior the first dose of study medication

          -  Has a history of (non-infectious) pneumonitis that required steroids or has current
             pneumonitis

          -  Has an active infection requiring systemic therapy

          -  Has a known history of Human Immunodeficiency Virus (HIV) infection

          -  Has a known history of Hepatitis B or known active Hepatitis C virus infection

          -  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 a known psychiatric or substance abuse disorder that would interfere with the
             participant's ability to cooperate with the requirements of the study

          -  Has had an allogenic tissue/solid organ transplant