Lenvatinib (E7080/MK-7902) in Combination With Pembrolizumab (MK-3475) vs. Standard Chemotherapy and Lenvatinib Monotherapy in Participants With Recurrent/Metastatic Head and Neck Squamous Cell Carcinoma That Progressed After Platinum Therapy and Immunotherapy (MK-7902-009/E7080-G000-228/LEAP-009)

Inclusion Criteria:

• Pathologically confirmed recurrent (not amenable to curative treatment with localand/or systemic therapies) or metastatic (disseminated) head and neck squamous cellcarcinoma (HNSCC) of the oral cavity, oropharynx, hypopharynx, and/or larynx that isconsidered incurable by local therapies

• Disease progression at any time during or after treatment with a platinum-containing (e.g., carboplatin or cisplatin) regimen

• Disease progression on or after treatment with a programmed cell death protein 1/programmed death-ligand 1 monoclonal antibody (anti-PD-1/PD-L1 mAb)

• Pre-study imaging that demonstrates evidence of disease progression based oninvestigator review of at least 2 pre-study images per RECIST 1.1, followinginitiation of treatment with a PD-1/PD-L1 inhibitor

• Measurable disease by computed tomography scan (CT) or magnetic resonance imaging (MRI) based on Response Criteria in Solid Tumors Version 1.1 (RECIST 1.1) asverified by blinded independent central review (BICR). Tumor lesions situated in apreviously irradiated area are considered measurable if progression has beendemonstrated in such lesions

• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 assessedwithin 7 days of the first dose of study intervention

• Male participants are eligible to participate if they agree to the following duringthe intervention period and for at least 1 week after the last dose of lenvatinib, 3months after the last dose of capecitabine and paclitaxel, and 6 months after thelast dose of docetaxel:

• Refrain from donating sperm

• Be abstinent from heterosexual intercourse as their preferred and usuallifestyle (abstinent on a long term and persistent basis) and agree to remainabstinent; or must agree to use contraception unless confirmed to beazoospermic

• Contraceptive use by men should be consistent with local regulations regardingthe methods of contraception for those participating in clinical studies

• A female participant is eligible to participate if she is not pregnant orbreastfeeding, and at least one of the following conditions applies:

• Is not a woman of childbearing potential (WOCBP)

• Is a WOCBP and using a contraceptive method that is highly effective (with afailure rate of <1% per year), with low user dependency or be abstinent fromheterosexual intercourse as their preferred and usual lifestyle (abstinent on along term and persistent basis), during the intervention period and for atleast 120 days post pembrolizumab or 1 month post lenvatinib, whichever occurslast (Arms 1 and 3), or during the intervention period and for at least 6months after the last dose of capecitabine, docetaxel, paclitaxel; and 2 monthsafter the last dose of cetuximab (Arm 2)

• Female participants who randomize to Arm 2 must also agree not to donate orfreeze/store eggs during the intervention period and for at least 6 monthsafter the last dose of capecitabine, docetaxel, paclitaxel; and 2 months afterthe last dose of cetuximab

• Adequately controlled blood pressure (BP) with or without antihypertensivemedications

• Participants who are hepatitis B surface antigen (HBsAg) positive are eligible ifthey have received hepatitis B virus (HBV) antiviral therapy for at least 4 weeksand have undetectable HBV viral load prior to randomization

• Participants with history of hepatitis C virus (HCV) infection are eligible if HCVviral load is undetectable at screening

• Adequate organ function

Exclusion Criteria:

• Disease that is suitable for local therapy administered with curative intent

• Life expectancy of less than 3 months and/or has rapidly progressing disease in theopinion of the treating investigator

• History of (noninfectious) pneumonitis/interstitial lung disease that requiredsteroids, or has current pneumonitis/interstitial lung disease

• Active infection requiring systemic therapy

• Diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (indosing exceeding 10 mg daily of prednisone equivalent) or any other form ofimmunosuppressive therapy within 7 days prior to the first dose of study drug

• Known active central nervous system (CNS) metastases and/or carcinomatous meningitis

• Known additional malignancy that is progressing or has required active systemictreatment within the past 3 years, except basal cell carcinoma of the skin, squamouscell carcinoma of the skin, superficial bladder cancer, or carcinoma in situ thathave undergone potentially curative therapy

• Active autoimmune disease that has required systemic treatment in the past 2 years

• Had an allogeneic tissue/solid organ transplant

• Known history of human immunodeficiency virus (HIV) infection

• History of any contraindication or has a severe hypersensitivity to any componentsof pembrolizumab, lenvatinib or SOC chemotherapy.

• Pre-existing ≥Grade 3 gastrointestinal or non-gastrointestinal fistula

• History of a gastrointestinal malabsorption or any other condition or procedure thatmay affect oral study drug absorption

• Had major surgery within 3 weeks prior to first dose of study interventions

• Clinically significant cardiovascular impairment within 12 months of the first doseof study drug

• Active tuberculosis

• Has difficulty swallowing capsules or ingesting a suspension orally, or by a feedingtube

• Prior treatment with lenvatinib

• Prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2weeks prior to Study Day 1 or has not recovered from adverse events (AEs) due to apreviously administered agent. Participants with endocrine-related AEs Grade ≤2requiring treatment or hormone replacement may be eligible

• Has received a live or live attenuated vaccine within 30 days prior to the firstdose of study intervention. Note: Administration of killed vaccines is allowed

• Previously treated with 4 or more systemic regimens given for recurrent/metastaticdisease

• Has received an investigational agent or has used an investigational device within 4weeks prior to study intervention administration

• Known psychiatric or substance abuse disorder that would interfere with theparticipant's ability to cooperate with the requirements of the study