Pembrolizumab/Vibostolimab Coformulation (MK-7684A) or Pembrolizumab/Vibostolimab Coformulation Plus Docetaxel Versus Docetaxel for Metastatic Non Small Cell Lung Cancer (NSCLC) With Progressive Disease After Platinum Doublet Chemotherapy and Immunotherapy (MK-7684A-002, KEYVIBE-002)

Inclusion Criteria: * Has a histologically or cytologically confirmed diagnosis of metastatic non-small cell lung cancer (NSCLC) * Has confirmation that epidermal growth factor receptor (EGFR), anaplastic lymphoma kinase (ALK), or reactive oxygen species (ROS) 1 directed therapy is not indicated as primary therapy * Has progressive disease (PD) on treatment with one prior anti-programmed cell death 1 (PD-1)/ programmed cell death ligand 1 (PD-L1) monoclonal antibody (mAb) administered either as monotherapy or in combination with other checkpoint inhibitors or other therapies * Retreatment with the same anti-PD-L1/PD-L1 mAb is acceptable in the overall course of treatment * Has PD as determined by the investigator after platinum doublet chemotherapy for metastatic disease * Has measurable disease defined as at least 1 measurable lesion by computed tomography (CT) or magnetic resonance imaging (MRI), based on Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) * Has provided tumor tissue for PD-L1 biomarker analysis from an archival sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated * Has a life expectancy of at least 3 months * Has an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1 assessed within 7 days prior to randomization * Male participants randomized to docetaxel are eligible to participant if they agree to refrain from donating sperm, and either 1) be abstinent from heterosexual intercourse; or 2) must agree to follow contraceptive guidance as per study protocol unless confirmed to be azoospermic during the intervention period and for at least 180 days after the last dose of docetaxel * Female participants must be not pregnant, not breastfeeding, and not be a woman of child-bearing potential (WOCBP). A WOCBP is eligible is she agrees to either use contraception, or be abstinent from heterosexual intercourse during the intervention period and for ≥120 days after the last dose of study intervention. If a WOCBP is randomized to docetaxel, she agrees not to donate eggs and either uses contraception or be abstinent from heterosexual intercourse during the treatment period and for ≥180 days after the last dose of docetaxel * Has adequate organ function Exclusion Criteria: * Has known active or untreated central nervous system (CNS) metastases and/or carcinomatous meningitis * Has a known history of an additional malignancy, except if the participant has undergone potentially curative therapy with no evidence of that disease recurrence for at least 3 years since initiation of that therapy * Has received docetaxel as monotherapy or in combination with other therapies * Has received previous treatment with another agent targeting the T-cell immunoreceptor with immunoglobulin \[Ig\] and immunoreceptor tyrosine-based inhibitory motif \[ITIM\] domains (TIGIT) pathway * Has received radiotherapy within 2 weeks of start of study intervention. One week washout is permitted for palliative radiation to non-CNS disease * Has received a live or live-attenuated vaccine within 30 days before the first dose of study intervention * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks before the first dose of study intervention * Has severe hypersensitivity (≥Grade 3) to docetaxel or pembrolizumab/vibostolimab coformulation 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 or any other form of immunosuppressive therapy within 7 days before the first dose of study intervention * Has interstitial lung disease, or history of pneumonitis requiring steroids for treatment * Has known history of active human immunodeficiency virus (HIV), Hepatitis B or Hepatitis C * Has had an allogenic tissue/solid organ transplant * Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study