A Study of TAK-676 With Pembrolizumab After Radiation Therapy to Treat a Number of Cancers

Inclusion Criteria:

1. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
2. Participants must have at least 2 measurable lesions (i.e. ≥10 mm longest diameter for extranodal lesions, ≥15 mm short axis for lymph nodes), with at least one inside and at least one other outside of the radiation field. The tumor outside the radiation field must be accessible for biopsy, and the participant must consent to tumor biopsy at screening and during treatment.
3. Participants must have pathologically confirmed (cytological diagnosis is adequate) advanced or metastatic NSCLC, TNBC, or SCCHN who have:

   * Received or been offered all established standard of care (SOC) treatment options for which they are eligible; and
   * Progressed on CPIs in a prior line of therapy.
4. Adequate bone marrow, renal and hepatic functions.
5. Left ventricular ejection fraction (LVEF) \>50%, as measured by echocardiogram or multiple-gated acquisition (MUGA) scan within 4 weeks before receiving the first dose of study drug.
6. Clinically significant toxic effects of previous therapy have recovered to Grade 1 (per NCI CTCAE, V5.0) or baseline, except for alopecia, Grade 2 peripheral neuropathy, and/or autoimmune endocrinopathies with stable endocrine replacement therapy.

Exclusion Criteria:

1. History of any serious cardiac or cerebrovascular conditions in the last 6 months, including uncontrolled congestive heart disease, unstable angina, myocardial infarction, hypertension greater than or equal to (≥) 160/100 millimeter of mercury (mmHg) in spite of optimal therapy, cardiac arrhythmias, pericardial effusion, cardiomyopathy, or symptomatic stroke. Chronic, stable atrial fibrillation on stable anticoagulation therapy, including low molecular weight heparin, will be allowed.
2. History of brain metastasis unless:

   * Clinically stable, (that is, treatment completed ≥4 weeks prior) following prior surgery, whole-brain radiation, or stereotactic radiosurgery, AND
   * Off corticosteroids.
3. Known history of uncontrolled autoimmune disorders, human immunodeficiency virus (HIV) infection, or other relevant congenital or acquired immunodeficiencies.
4. Chronic, active hepatitis (example, participants with known hepatitis B surface antigen seropositive and/or detectable hepatitis C virus \[HCV\]-ribonucleic acid \[RNA\]).
5. Treatment with any investigational products and systemic anticancer drugs (including vascular endothelial growth factor (VEGF) inhibitors), within 14 days or 5 half-lives, whichever is shorter, before Cycle 1 Day 1 (C1D1) of study drugs.
6. Prior radiation to lesions chosen for biopsy or response assessment.
7. Prior radiation to lesions other than those chosen for radiation therapy or biopsy in the current protocol within 4 weeks of C1D1 of study drug(s).
8. Use of systemic corticosteroids or other immunosuppressive therapy, concurrently or within 7 days of start of radiation therapy, with the following exceptions:

   * Topical, intranasal, inhaled, ocular, intra-articular, and/or other nonsystemic corticosteroids.
   * Physiological doses of replacement steroid therapy (example, for adrenal insufficiency).
9. Receipt of live attenuated vaccine (example, tuberculosis Bacillus Calmette-guerin \[BCG\] vaccine, oral polio vaccine, measles, rotavirus, yellow fiver) within 28 days of C1D1 of study drug(s).
10. Recipients of allogeneic or autologous stem cell transplantation or organ transplantation.
11. Ongoing Grade ≥2 infection or participants with Grade ≥2 fever of malignant origin.
12. Fridericia's corrected QT interval (QTcF) \>450 milliseconds (msec) (males) or \>475 msec (females) on a 12-lead electrocardiogram (ECG) during the screening period.
13. Grade ≥2 hypotension (that is, hypotension for which nonurgent intervention is required) at screening or during C1D1 pre-dose assessment.
14. Oxygen saturation less than (\<) 92% on room air at screening or during C1D1 predose assessment.
15. Use of medications that are known clinical organic anion transporting polypeptide 1B1 (OATP1B1) and/or OATP1B3 inhibitors, concurrently or within 14 days of C1D1 of study drugs.
16. Current smoker.
17. Vaping within 90 days of C1D1 of study drugs.
18. Current diagnosis of pneumonitis, interstitial lung disease, severe chronic obstructive pulmonary disease (COPD), idiopathic pulmonary fibrosis, other restrictive lung diseases, acute pulmonary embolism, or Grade ≥2 pleural effusion or ascites not controlled by tap or requiring indwelling catheters.
19. Treated with other stimulator of interferon genes (STING) agonists/antagonist and toll-like receptors agonists within the past 6 months.