A Study Comparing TAK-928 With Docetaxel in Adults With Non-Small Cell Lung Cancer

Lung cancer is one of the most common forms of cancer. One common type is non-small cell lung cancer (NSCLC). NSCLC happens when abnormal cells in the lungs grow too fast. This can stop the lungs from working normally. NSCLC can be divided into types based on where cancer starts. Some NSCLC starts in the cells that line the larger airways near the center of the lungs. This is called squamous NSCLC. Other NSCLC often starts in the outer parts of the lungs, in cells that make mucus. This is called nonsquamous NSCLC. This study focuses on squamous and nonsquamous NSCLC in later stages (advanced). This means that the cancer has spread to other parts of the body (metastatic) or cannot be removed with surgery (unresectable). People with unresectable, advanced or metastatic squamous or nonsquamous NSCLC often get treatment with immunotherapy and/or platinum-based chemotherapy (such as cisplatin or carboplatin). Immunotherapy helps the body's germ-fighting (immune) system fight cancer. Chemotherapy kills cancer cells or slows their growth. Over time, these treatments may stop working and the cancer can get worse. Researchers are looking for ways to make immunotherapy work better. One approach is to help the immune system recognize cancer more easily by activating certain cells, called T cells, to attack and kill the tumor cells. TAK-928 is designed to attach to T cells in the tumor. This may make the T-cells more active and increase their number. This may help the body fight the cancer and destroy tumor cells. The main aim of this study is to learn how well TAK-928 works and compares with the usual treatment (also called standard of care), docetaxel, in adults with unresectable, advanced or metastatic squamous or nonsquamous NSCLC. Another aim is to learn how safe TAK-928 is in adults with NSCLC. The participants can be treated for up to 2 years (24 months). Total treatment duration can vary depending on how a participant responds, side effects, or other reasons. Researchers will check a participant's condition until the treatment is ended. During the study, participants will visit the study clinic several times.

Inclusion Criteria: 1. Must be able to understand and willing to sign the written ICF and be able to comply with the visit schedule and related procedures specified in the protocol. 2. Male or female participants must be at least 18 years old or the legal age of majority in their country, whichever is greater. Note: For the Japan-specific SRI part, participants must be Japanese residing in Japan. 3. (a) Squamous NSCLC: Have locally unresectable advanced or metastatic histologically or cytologically confirmed squamous NSCLC. Mixed small cell carcinoma, or other pathological components are excluded. (b) Nonsquamous NLSCLC: Have locally unresectable advanced or metastatic histologically or cytologically confirmed nonsquamous NSCLC. Mixed small cell carcinoma, or other pathological components are excluded. (c) For Japan-specific SRI part: Have metastatic or unresectable solid tumors. 4. Have had radiographic disease progression on or after prior treatment with anti-PD-1/PD-L1 therapy and platinum-based doublet chemotherapy (for example, carboplatin and paclitaxel), given either concurrently or sequentially. A total exposure of \>=6 weeks of prior anti-PD-1/PD-L1 therapy is required. Eligible participants include those that have: * Received platinum-based chemotherapy in combination with anti-PD-1/PD-L1 therapy as only prior line of therapy. OR * Received platinum-based chemotherapy and anti-PD-1/PD-L1 therapy sequentially (in either order) as the only 2 prior lines of therapy. Note: (1) Participants that are ineligible to receive platinum-based doublet chemotherapy may still be eligible for trial enrollment, assuming all other criteria are met. (2) For the Japan-specific SRI part only: participants' disease must be refractory OR participants must be intolerant to indication-specific SOC treatment. 5. Participants who have received prior anti-PD-1/PD-L1 therapy with curative intent for locally advanced disease are eligible if they meet either of the following criteria: * Received prior platinum-based chemotherapy with or without radiotherapy with maintenance anti-PD-1/PD-L1 therapy for Stage III disease and radiographic recurrence/progression within 6 months from the last dose of platinum-based chemotherapy. OR * Received prior peri-operative platinum-based chemotherapy with maintenance anti-PD-1/PD-L1 therapy for resectable Stage II/III and have radiographic recurrence within 6 months from the last dose of platinum-based chemotherapy. Note: 1) Participants that are ineligible to receive platinum-based doublet chemotherapy may still be eligible for trial enrollment, assuming all other criteria are met. (2) For the Japan-specific SRI part only: This criterion is not applicable for Japanese participants enrolled in the SRI part of the trial. 6\. Provide formalin-fixed tumor tissue specimen. Fresh biopsies are preferred but archival specimens collected within 2 years before signing the informed consent form are acceptable (blocks or 10-15 unstained slides sectioned 4-5 microns in thickness, if tissue slides, they must be sectioned from blocks \=3 months. 10. WOCBP must take a urine or serum pregnancy test, highly sensitive tests are required where available based on region and must test negative for trial inclusion. WOCBP must agree to use at least 1 form of highly effective contraception and 1 barrier method of contraception during the entire course of treatment and for 6 months after the last dose of trial treatment. Fertile men must agree to use a condom, preferably combined with at least 1 form of acceptable contraception for any WOCBP partner(s) during the entire course of treatment and for 6 months after the last dose of trial intervention. 11\. Lactating women must agree to strictly abstain from breastfeeding during the entire Treatment Period and for 6 months after the treatment. Exclusion Criteria: 1. Women who are pregnant or breastfeeding, or intending to become pregnant before, during, or within 6 months after the last dose of any trial intervention. WOCBP not using and/or not willing to use at least 1 form of highly effective method of contraception and 1 barrier method of contraception or fertile men with WOCBP partner(s) not using and/or not willing to use at least 1 form of acceptable contraception. 2. (a) Squamous NSCLC: Known actionable genomic alteration, including any of the following driver gene mutations: * EGFR: including exon 19 deletion, exon 21 L858R, exon 20 T790M, exon 20 S768I, exon 21 L861Q, exon 18 G719X, and exon 20 insertion mutations. * ALK rearrangement. * ROS proto-oncogene 1, ROS1 rearrangement. * B-Raf proto-oncogene, serine/threonine kinase (BRAF) V600E mutation. * NTRK 1/2/3 fusion. * MET proto-oncogene, MET exon 14 skipping mutation. * RET proto-oncogene (RET) rearrangement. * V-erb-b2 avian erythroblastic leukemia viral oncogene homolog 2 (ERBB2, also known as HER2) mutation. Note: (1) It is not mandatory to have undergone driver gene testing for participants with squamous NSCLC. (2) KRAS mutations are not exclusionary. (b) Nonsquamous NSCLC: Must have documentation of prior testing demonstrating negative AGA status for any of the following driver gene mutations: * EGFR: including exon 19 deletion, exon 21 L858R, exon 20 T790M, exon 20 S768I, exon 21 L861Q, exon 18 G719X, and exon 20 insertion mutations. * ALK rearrangement. * ROS1 rearrangement. * Any other driver gene mutations listed here are excluded if known to be present, but routine testing for these or other known actionable genomic alterations is not required: BRAF V600E mutation; NTRK 1/2/3 fusion; MET exon 14 skipping mutation; RET rearrangement; and ERBB2, also known as HER2 mutation. Note: KRAS mutations are not exclusionary. (c) For Japan-specific SRI part: This criterion is not applicable for Japanese participants enrolled in the SRI part. 3. Participants with enlarging or symptomatic brain metastases are excluded from the trial. Participants who are neurologically, clinically and radiologically stable \>=2 weeks after definitive treatment for brain metastases and/or participants with small (sum of all brain lesions: ≤3 cm), asymptomatic, incidental, untreated brain metastases may participate in this trial as long as they meet certain criteria as defined in the protocol. 4. Presence of any of the following hematologic abnormalities at baseline\*: * Hemoglobin \=480 msec. * Uncontrolled hypertension despite standard treatment. * History of myocarditis. * Left ventricular ejection fraction \=levels consistent with acute myocardial infarction as defined by laboratory-specific criteria. Participants with isolated Grade 1 elevated cardiac enzymes require cardiology clearance and consultation with the sponsor's medical monitor to confirm absence of ongoing myocardial/ischemic disease. 11. History of or current ILD; history or current presence of the following lung diseases requiring corticosteroid therapy: pulmonary fibrosis, and drug-related, immune-related or radiation pneumonitis; current active pulmonary infection requiring anti-infective therapy; active pulmonary TB within 1 year prior to enrollment; severely impaired pulmonary function, including but not limited to the following:, severe asthma or severe chronic obstructive pulmonary disease within 3 months prior to randomization; autoimmune, connective tissue, or inflammatory diseases involving the lungs (such as rheumatoid arthritis, Sjögren's disease, and sarcoidosis); previous unilateral pneumonectomy. Note: Participants with a positive IGRA and negative chest imaging for active pulmonary TB (that is, participants with a history of latent TB) may enroll if they have completed appropriate definitive treatment for latent TB prior to enrollment in the trial (C1D1). Participants with a history of active TB may enroll if they have completed appropriate definitive treatment for active TB more than 1 year before enrollment in the trial (C1D1) and chest imaging at the time of screening is negative for active disease. 12. History of severe, poorly controlled allergies, asthma or atopic dermatitis (except for atopic dermatitis caused by immunotherapy). Note: remote history of childhood asthma is not exclusionary. 13. Uncontrolled third space effusion requiring repeated drainage, such as pleural effusion, abdominal effusion, or pericardial effusion. 14. Current or recent significant gastrointestinal disease or condition, including: * Flare of inflammatory bowel disease (within 6 months prior to the first dose of the investigational product). * Grade \>=2 diarrhea CTCAE V5.0 within 2 weeks prior to the first dose of the investigational product. 15. Active autoimmune disease requiring systemic treatment (for example, use of disease modifying drugs, corticosteroids \>10 milligrams (mg) daily equivalent of prednisone, biologics or immunosuppressants) within 2 years before the first dose. Note: Replacement therapies (for example, thyroxine, insulin, or physiological corticosteroids for adrenal or pituitary insufficiency) are not considered systemic treatments and are not exclusionary. 16. Known history of allogeneic organ transplantation and/or allogeneic hematopoietic stem cell transplantation. 17. Known or suspected allergy to the investigational product and any excipients. Known or suspected severe hypersensitivity reactions to docetaxel or to drugs formulated with polysorbate 80. 18. Prior history of significant toxicity related to ICI administration that required permanent discontinuation of this therapy. 19. Unresolved Grade \>1 toxicity related to any previous antitumor therapy (excluding alopecia, asthenia, hypothyroidism requiring only thyroid hormone replacement therapy (HRT), hyperglycemia requiring only insulin replacement therapy, adrenal insufficiency requiring physiological corticosteroid replacement, electrolyte abnormalities requiring only symptomatic treatment, and other conditions not affecting the investigational product treatment as assessed by the investigator). 20. Have not adequately recovered from previous surgery or have undergone any major surgery, within 4 weeks before the first dose of investigational product. 21. Uncontrolled tumor-related pain or symptomatic hypercalcemia. 22. Uncontrolled human immunodeficiency virus (HIV), active syphilis, active hepatitis B virus (HBV), or hepatitis C virus (HCV). * Participants who are HIV-positive must have CD4 \>=350 cells per microliter (cells/µL) and must be on established highly active antiretroviral therapy (ensure no expected drug-drug interactions) for at least 4 weeks with an HIV viral load \