Inclusion Criteria:

• At least 18 years of age.
• Participants must have histologically confirmed locally advanced, recurrent or metastatic solid tumor malignancies that cannot be treated with curative intent (surgery or radiotherapy).
• Participants must have progressed on or be intolerant of available standard of care treatment options or have disease for which there is no standard of care treatment available.
• At least 2 lesions of measurable disease.
• Willingness to undergo biopsies.
• Demonstrated adequate organ function within 14 days of Cycle 1 Day 1 (C1D1).
• Life expectancy >12 weeks as determined by the Investigator.
• Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2.
• Participants who have undergone treatment with anti-PD-1, anti-PD-L1, or anti-CTLA-4 antibody must have at least 4 weeks from the last dose of antibody and evidence of disease progression per investigator assessment before enrollment.
• Participants who have previously received an immune checkpoint inhibitor prior to enrollment must have any immune related toxicities resolved to ≤Grade 1 or baseline (prior to the checkpoint inhibitor) to be eligible.
• Female and male participants of childbearing potential who are sexually active must agree to use highly effective methods of contraception.

Exclusion Criteria:

• Participants who have been previously treated with a TLR agonist (excluding topical agents for unrelated disease) are not eligible.
• Participants who have received systemic interferon alpha within the previous 24 weeks prior to enrollment are not eligible.
• Other active malignancies within the last 2 years are excluded.
• Active autoimmune diseases, regardless of need for immunosuppressive treatment at the time of screening, with the exception of patients well controlled on physiologic endocrine replacement.
• Systemic immunosuppressive treatment with the exception for patients on corticosteroid taper (for example, for chronic obstructive pulmonary disease exacerbation). Participants cannot start dosing on study until steroid dose is at or lower than 10 mg per day prednisone or equivalent.
• Women who are breastfeeding or have a positive serum pregnancy test during screening or within 48 hours prior to C1D1 are not eligible.
• Vaccination with live, attenuated vaccines within 4 weeks of enrollment.
• Symptomatic central nervous system metastases.
• Known bleeding disorder that is deemed to place the patient at unacceptable risk for bleeding complications from intratumoral injections or biopsies.
• Known hypersensitivity to any component of TransCon TLR7/8 Agonist or pembrolizumab.
• Any uncontrolled bacterial, fungal, viral, or other infection.
• Treatment with any other anti-cancer systemic treatment (approved or investigational) or radiation therapy within 4 weeks of first dosing on study is not allowed.
• Significant cardiac disease
• A marked baseline prolongation of QT/QTc interval (e.g., repeated demonstration of a QTc interval >480 milliseconds (ms) (CTCAE grade 1) using Fredericia's QT correction formula.
• A history of additional risk factors for Torsades de Pointes (TdP) (e.g., heart failure, clinically significant hypokalemia, family history of Long QT Syndrome).
• The use of concomitant medications that prolong the QT/QTc interval within 14 days of enrollment.
• Positive for HIV or with active hepatitis B or C infection.