Inclusion Criteria:

          1. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.

          2. Life expectancy >12 weeks, as assessed by the investigator.

          3. TAK-676 SA:

             o With histologically confirmed (cytological diagnosis is acceptable) advanced or
             metastatic solid tumors that have no standard therapeutic options or are intolerant to
             these therapies.

          4. TAK-676 in combination with pembrolizumab:

             o With histologically confirmed (cytological diagnosis is acceptable) advanced or
             metastatic solid tumors that have no standard therapeutic options or are intolerant to
             them, including:

               -  Tumors that have relapsed or are refractory to anti-programmed cell death protein
                  1 (anti-PD-1)/anti-programmed cell death ligand 1 (anti-PD-L1) therapy.

               -  Tumors that are naive to anti-PD-1/ anti-PD-L1 therapy.

          5. Adequate bone marrow, renal, hepatic and cardiac functions.

          6. 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.

          7. Clinically significant toxic effects of previous therapy have recovered to Grade 1
             (per NCI CTCAE Version 5.0) or baseline, except for alopecia, Grade 2 peripheral
             neuropathy, and/or autoimmune endocrinopathies with stable endocrine replacement
             therapy.

          8. Once peripheral evidence of TAK-676 pharmacodynamic stimulation of the innate and/or
             adaptive immune system is observed in the blood and/or clinical response/partial
             response (CR/PR) is observed in at least 1 participant, subsequent participants must:

               -  Have at least 1 lesion amenable for biopsy.

               -  Agree to have 2 tumor biopsies: 1 during the screening period and 1 while on
                  TAK-676 treatment.

          9. Must have at least 1 RECIST v.1.1-evaluable (measurable or nonmeasurable) lesion.

         10. Pharmacokinetic (PK)/pharmacodynamic blood must be drawn on a peripherally-inserted
             catheter. TAK-676 is preferentially administered through a central line, but
             peripheral infusion is acceptable. If a peripheral line is used for TAK-676 and/or
             pembrolizumab infusion, it must be separate than the one used for PK/ pharmacodynamic
             collection.

        Exclusion Criteria:

          1. Corrected QT interval by Fredericia (QTcF) greater than (>) 450 milliseconds (men) or
             >475 milliseconds (women) on a 12-lead ECG during the screening period.

          2. Grade greater than or equal to (>=) 2 hypotension (that is, hypotension for which
             nonurgent intervention is required) at screening or during C1D1 predose assessment.

          3. Oxygen saturation less than (<) 92 percent (%) on room air at screening or during C1D1
             predose assessment.

          4. Treated with other STING agonists/antagonist and toll-like receptors agonists within
             the past 6 months.

          5. Active vaping within 90 days of C1D1 of study drug(s).

          6. Active smoking.

          7. Current history of pneumonitis, interstitial lung disease, severe chronic obstructive
             pulmonary disease, 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.

          8. History of brain metastasis unless:

               -  Clinically stable (that is, >=6 weeks) following prior surgery, whole-brain
                  radiation, or stereotactic radiosurgery, AND

               -  Off corticosteroids.

          9. Ongoing Grade >= 2 infection or participants with Grade >=2 fever of malignant origin.

         10. Chronic, active hepatitis (example: participants with known hepatitis B surface
             antigen seropositive and/or detectable hepatitis C virus [HCV]-RNA).

         11. For participants in the SA arm only: refusal of standard therapeutic options.

         12. For participants in the combination arm only: contraindication and/or intolerance to
             the administration of pembrolizumab.

         13. Concurrent chemotherapy, immunotherapy (except for pembrolizumab in the combination
             arm), biologic, or hormonal therapy (except for adjuvant endocrine therapy for a
             history of breast cancer). Concurrent use of hormones for noncancer-related conditions
             is acceptable (except for corticosteroid hormones).

         14. Radiation therapy within 14 days (42 days for radiation to the lungs) and/or systemic
             treatment with radionuclides within 42 days before C1D1 of study drug(s). Participants
             with clinically relevant ongoing pulmonary complications from prior radiation therapy
             are not eligible.

         15. Use of systemic corticosteroids or other immunosuppressive therapy, concurrently or
             within days of C1D1 of study drug(s), with the following exceptions:

               -  Topical, intranasal, inhaled, ocular, and/or intra-articular corticosteroids.

               -  Physiological doses of replacement steroid therapy (example: for adrenal
                  insufficiency).

         16. Use of medications that are known clinical OATP1B1 and/or OATP1B3 inhibitors,
             concurrently or within 14 days of C1D1 of study drug(s).

         17. Receipt of live attenuated vaccine within 28 days of C1D1 of study drug(s).

         18. Recipients of allogeneic or autologous stem cell transplantation or organ
             transplantation.