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. This study focuses on 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 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 and make them more active and abundant. 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 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) 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 informed consent form (ICF), 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. For Japan-specific safety run-in (SRI) part of the trial, participants must be Japanese residing in Japan.

3. Have locally unresectable advanced or metastatic histologically or cytologically confirmed squamous NSCLC. Mixed small cell carcinoma, or other pathological components are excluded.

   Note: For Japan-specific SRI only: Participants' histology is not restricted to squamous NSCLC and may include all metastatic or unresectable solid tumor participants.

4. Have had 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. Eligible participants include those that have:

   - Received platinum-based chemotherapy in combination with anti-PD-1/PD-L1 therapy as the 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: For Japan-specific SRI only: Participants must be refractory OR intolerant to standard of care (SOC) treatment.

5. Participants that 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 relapsed/progressed 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 relapsed within 6 months from the last dose of platinum-based chemotherapy.

   Note: For Japan-specific SRI 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 less than or equal to (<=) 2 months from date of consent). Formalin-fixed paraffin-embedded (FFPE) blocks are preferred for submission; slides should be sent only if there is a local regulation preventing submission of the FFPE block. Ideally, the archival specimen should be collected subsequent to the most recent systemic therapy.

   Note: For Japan-specific SRI only: Collection of tumor tissue specimen is not required for Japanese participants enrolled in the SRI part of the trial.

7. Have at least 1 measurable lesion (target lesion) by computed tomography (CT) or magnetic resonance imaging (MRI) according to Response Evaluation Criteria in Solid Tumors (RECIST) V1.1. Lesions that have previously received radiotherapy or intratumoral injection can only be used as measurable lesions if they show progression after treatment (either pathologically confirmed or with observation of radiographic progression more than 3 months after treatment) as per RECIST V1.1.

8. Eastern Cooperative Oncology Group (ECOG) performance status (PS) score of 0 or 1.

9. Expected survival time greater than or equal to (>=) 3 months.

10. Women of childbearing potential (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. Note: If in the investigator's judgment, the participant may be pregnant based on the physician's medical interview or other information, the participant will be excluded from the trial irrespective of a negative pregnancy test.

2. Known actionable genomic alteration, including any of the following driver gene mutations:

   • Epidermal growth factor receptor (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.
   • Kirsten rat sarcoma virus (KRAS) G12C mutation.
   • Anaplastic lymphoma kinase (ALK) rearrangement.
   • ROS proto-oncogene 1, receptor tyrosine kinase (ROS1) rearrangement.
   • B-Raf proto-oncogene, serine/threonine kinase (BRAF) V600E mutation.
   • Neurotrophic tyrosine receptor kinase (NTRK) 1/2/3 fusion.
   • MET proto-oncogene, receptor tyrosine kinase (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: (a) It is not mandatory to have undergone driver gene testing. (b) For Japan-specific SRI only: This criterion is not applicable for Japanese participants enrolled in the SRI part of the trial.

3. Participants with enlarging or symptomatic brain metastases are excluded from the trial. Participants who are neurologically, clinically and radiologically stable >=4 weeks after definitive treatment for brain metastases and participants with small, asymptomatic, incidental, untreated brain metastases that remain radiographically stable >=4 weeks after initial identification may participate in this trial as long as they meet all of the following criteria:

   • No metastases to meninges, midbrain, pons, medulla oblongata (leptomeningeal metastases), or cerebellar metastases.
   • No compression of the aqueduct of Sylvius, no compression of the third or fourth ventricle.
   • No participant with epidural spinal cord compression or spinal cord metastases.
   • Participants must be off steroids for at least 7 days for CNS disease. Systemic steroids of <=10 milligrams per day (mg/day) of prednisone or equivalent are acceptable if needed for other indications.
   • CNS-related symptoms must be stable >=14 days prior to randomization
   • Brain metastases should not be included as RECIST V1.1 target lesions

4. Presence of any of the following hematologic abnormalities at baseline*:

   • Hemoglobin <9 grams per deciliter (g/dL).
   • Absolute neutrophil count (ANC) <1,500 per cubic millimeters (mm^3).
   • Platelet (PLT) count <100 x 10^3/mm^3. *"Baseline" is defined as the last available observation prior to the first dose of investigational product. Note: Participants must not receive supportive treatments such as blood products (including RBC suspension, apheresis platelets, cryoprecipitation, and so on.) within 7 days of confirming eligibility. Erythropoietin or colony-stimulating factors must not be administered within 28 days of confirming eligibility.

5. Presence of any of the following serum chemistry abnormalities at baseline:

   • Total bilirubin greater than (>) 1.5×upper limit of normal (ULN) except for participants with Gilbert's syndrome with serum bilirubin <=3×ULN or if concurrent conjugated bilirubin <=ULN.
   • Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) >3×ULN; for liver metastasis, AST or ALT >5×ULN.
   • Creatinine clearance (CrCl) <30 milliters per minute (mL/min); the Cockcroft-Gault formula is used to calculate CrCl (using ideal body weight for obese participants and actual body weight for non-obese participants).
   • Albumin <30 grams per liter (g/L).

6. Presence of any of the following coagulation parameter abnormalities at baseline:

   • International normalized ratio (INR) >1.5×ULN (>3×ULN if on stable dose anticoagulation).
   • Partial thromboplastin time (PTT; or activated partial thromboplastin time [aPTT]) >1.5×ULN (>3×ULN if on stable-dose anticoagulation).

7. History of deep venous thrombosis, pulmonary embolism, or any other serious thromboembolic events within 30 days prior to enrollment (implantable port or catheter-related thrombosis, or superficial venous thrombosis are not considered "serious" thromboembolisms). Participants with a history of serious thromboembolic event must be asymptomatic and on stable anticoagulation therapy (if such therapy is deemed necessary by the treating physician).

8. Active uncontrolled bleeding, known bleeding diathesis, or significant concern for risk of acute life-threatening bleeding (for example, radiographic evidence that tumor invades large blood vessels or has unclear boundaries with a major vessel [including aorta, left pulmonary artery, right pulmonary artery, pulmonary vein, superior vena cava, inferior vena cava, and so on], or the investigator judges that the tumor is very likely to invade major vessels with the potential to cause fatal bleeding during the duration of the trial).

9. Presence of clinically significant cardiovascular or cerebrovascular diseases, including:

   • Symptomatic, clinically unstable arrhythmia or arrhythmia requiring clinical intervention.
   • Severe conduction disorders (such as third-degree atrioventricular block and bundle branch block).
   • QT interval corrected for heart rate (QTc interval, calculated using Fridericia's formula) >=480 milliseconds (msec).
   • Uncontrolled hypertension (systolic blood pressure >=160 millimeters of mercury (mmHg) or diastolic blood pressure >=100 mmHg) despite standard treatment.
   • History of myocarditis.
   • Left ventricular ejection fraction <50 percent (%).
   • Congestive heart failure requiring treatment.
   • Class II to IV cardiac insufficiency according to the New York Heart Association functional classification.
   • History of acute coronary syndrome (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to the first dose of investigational product.
   • Cerebrovascular accident or transient ischemic attack within 6 months before the first dose of the investigational product.
   • History of seizures unless controlled on stable dose of antiseizure medications.

10. Cardiac enzymes >=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 interstitial lung disease (ILD), pulmonary fibrosis, and drug-related, immune-related and radiation pneumonitis; current active pulmonary infection requiring anti-infective therapy; active pulmonary tuberculosis (TB) within 1 year prior to enrollment; severely impaired pulmonary function, including but not limited to the following: pulmonary embolism, severe asthma or 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 interferon-gamma release assay (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, pericardial effusion, so on.

    Note: Participants with the following conditions may be enrolled:

    • Not requiring active drainage.
    • No significant increase in effusion after stopping drainage determined using at least 2 ultrasound examinations at least 7 days apart.

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 Common Terminology Criteria for Adverse Events (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, 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 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 immune checkpoint inhibitor (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 steroid 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 <400 copies per milliliter (copies/mL).
    • Participants with positive results consistent with an untreated syphilis infection cannot enroll.

    Note: Testing with either a treponemal [for example, Treponema Pallidum hemagglutination TPHA or Treponema Pallidum particle agglutination TPPA test] or nontreponemal [for example, rapid plasma reagin (RPR) or Venereal Disease Research Laboratory test] assay is acceptable. An initial positive test should be confirmed with an assay using the alternate testing approach (for example, treponemal followed by nontreponemal or vice versa). If the second test is negative, the participant may enroll in the trial.

    • Participants with positive hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb) should undergo HBV DNA testing. If the HBV DNA copy number is <=2.5×10^3 copies/mL or <=500 international units per milliliter (IU/mL) or below the lower limit of detection, the participant can be enrolled. Participants who are HBsAg (+) should receive anti-HBV treatment throughout the treatment period to avoid viral activation. For participants with anti-hepatitis B core antibody (anti-HBcAb) (+), HBsAg (-), anti-HBs (-), and HBV viral load (-), prophylactic anti-HBV treatment can be considered but is not required; however, close monitoring for viral reactivation is required.
    • Participants with positive HCV serology results must have an HCV RNA viral load that is negative or below the lower limit of detection.
    • Participants who have received definitive HCV treatment and have undetectable viral load results are allowed.

23. Serious/active/uncontrolled infection, infection requiring systemic intravenous antibiotics, or fever of unknown origin (>=38 degree celsius [°C]) within 2 weeks before the first dose of investigational product.

24. History or current evidence of any disease, treatment, or laboratory abnormality that, in the judgment of the investigator, could compromise the safety of the participant, interfere with obtaining informed consent, affect participant compliance, or affect safety evaluations of the investigational product.

25. Psychiatric illness, altered mental status, or drug abuse that prevents understanding of the informed consent process and/or completion of required trial-related evaluations.

26. Unable to meet protocol requirements for known or foreseeable reasons per investigator judgement.

27. Diagnosed with other pathologically confirmed malignancies within 5 years prior to informed consent, with the exception of radically treated basal cell carcinoma of the skin, squamous cell carcinoma of the skin, carcinoma in situ, localized prostate cancer, papillary thyroid cancer, and other radically treated malignancies with no known active disease for at least 2 years prior to enrollment and with a very low risk of recurrence.

28. Received any of the following excluded medications or treatments:

    • Docetaxel.
    • Received more than 1 anti-PD-1/PD-L1 therapy in the metastatic or recurrent unresectable locally advanced setting. Prior anti-PD-1/PD-L1 therapy in the curative locally advanced setting followed by anti-PD-1/PD-L1 therapy in the metastatic or recurrent unresectable locally advanced setting is allowed, not to exceed 2 prior lines of anti-PD-1/PD-L1 therapy in total.
    • Systemic antitumor therapy except anti-PD-1/PD-L1 therapy and platinum-based doublet chemotherapy including but not limited to bispecific antibodies, targeted therapy, antibody drug conjugate, cell therapies, and other ICIs.

Note: For Japan-specific SRI only: The above listed 3 limitations regarding prior systemic antitumor therapy do not apply to participants enrolled in the Japan-specific SRI cohorts.

• Interleukin (IL)-2 or IL-15 cytokines or related therapies.
• Chemotherapy within 2 weeks or 5 half-lives (whichever is longer) before the first dose of investigational product without delayed toxicity.
• Antitumor antibody therapy (excluding antibody drugs such as denosumab for the treatment of bone metastases) within 4 weeks before the first dose of the investigational product.
• Palliative radiotherapy within 2 weeks prior to the first dose of investigational product.
• Live vaccine within 28 days prior to the first dose of investigational product.
• Immunosuppressive or systemic steroid therapy (>10 mg/day of prednisone or equivalent) within 2 weeks prior to the first dose of investigational product.
• Received traditional Chinese medicine with potential antitumor activity or known antitumor indications within 1 week before the first dose of the investigational product.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.