Inclusion Criteria:

          -  Subject must be >=18 years of at the time of signing the informed consent.

          -  Histological documentation of advanced solid tumor.

          -  Archival tumor tissue obtained at any time from the initial diagnosis to study entry.
             Although a fresh biopsy obtained during screening is preferred, archival tumor
             specimen is acceptable if it is not feasible to obtain a fresh biopsy. Subjects
             enrolled in a PK/Pharmacodynamic Cohort must provide a fresh biopsy of a tumor lesion
             not previously irradiated during the screening period and must agree to provide at
             least one additional on-treatment biopsy.

          -  Disease that has progressed after standard therapies or for which standard therapy is
             otherwise unsuitable (example, intolerance).

          -  Measurable disease, that is, presenting with at least 1 measurable lesion per Response
             Evaluation Criteria in Solid Tumors (RECIST version 1.1).

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1.

          -  Life expectancy of at least 12 weeks.

          -  Adequate organ function.

          -  In France, a subject will be eligible for inclusion in this study only if either
             affiliated to or a beneficiary of a social security category.

          -  Male or female subjects will be included. A female subject is eligible to participate
             if she is not pregnant, not breastfeeding, and at least 1 of the following conditions
             applies: a) Not a woman of childbearing potential (WOCBP) OR b). A WOCBP who agrees to
             follow the contraceptive guidance during the treatment period and for at least 120
             days after the last dose of study treatment.

          -  Capable of giving signed informed consent which includes compliance with the
             requirements and restrictions specified.

        Additional Inclusion criteria for Subjects in Part 2a (GSK3174998 expansion) and Part 2b
        (GSK3359609 expansion):

          -  Histological or cytological documentation of squamous cell carcinoma of the head and
             neck (SCCHN) (oral cavity, oropharynx, hypopharynx, or larynx) that is recurrent,
             locally advanced, or metastatic and is not amenable to curative treatment options,
             surgery or definitive chemoradiation therapy.

          -  Received, ineligible for, or otherwise unsuitable for platinum-based therapy and
             anti-Programmed death receptor-1 (PD-1)/programmed death-ligand 1 (PD-L1) therapy

          -  Received no more than 3 prior lines of systemic therapy for metastatic disease.

        Additional Inclusion Criteria for Subjects in Part 2c (pembrolizumab expansion):

          -  Histological or cytological documentation of SCCHN (oral cavity, oropharynx,
             hypopharynx, or larynx) that is recurrent, locally advanced, or metastatic and is not
             amenable to curative treatment options, surgery or definitive chemoradiation therapy.

          -  Received no more than 2 prior lines of systemic therapy for metastatic disease.

        Exclusion Criteria:

          -  Malignancy other than disease under study with the exception of those from which the
             subject has been disease-free for more than 2 years and not expected to affect the
             safety of the subject or the endpoints of the trial.

          -  Symptomatic central nervous system (CNS) metastases or asymptomatic CNS metastases
             that have required steroids within 2 weeks prior to first dose of study treatment.

          -  Active autoimmune disease that has required systemic disease modifying or
             immunosuppressive treatment within the last 2 years. Replacement therapy (example,
             thyroxine or physiologic corticosteroid replacement therapy for adrenal or pituitary
             insufficiency) is permitted.

          -  Concurrent medical condition requiring the use of systemic immunosuppressive treatment
             within 28 days before the first dose of study treatment.

          -  Known human immunodeficiency virus infection.

          -  Current unstable liver or biliary disease per investigator assessment defined by the
             presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal or
             gastric varices, persistent jaundice, or cirrhosis.

          -  Presence of Hepatitis B surface antigen (HBsAg) at screening or within 3 months prior
             to first dose of study treatment.

          -  Positive Hepatitis C test result at screening or within 3 months prior to first dose
             of study treatment.

          -  QT interval corrected for heart rate according to Fridericia's formula (QTcF) >450
             milliseconds (msec) or QTcF >480 msec for subjects with bundle branch block

          -  Recent history (within the past 6 months) of acute diverticulitis, inflammatory bowel
             disease, intra-abdominal abscess, or gastrointestinal obstruction.

          -  Recent history of allergen desensitization therapy within 4 weeks of starting study
             treatment.

          -  History of severe hypersensitivity to monoclonal antibodies (mAbs).

          -  History or evidence of cardiovascular (CV) risk including any of the following: a)
             Recent (within the past 6 months) history of serious uncontrolled cardiac arrhythmia
             or clinically significant ECG abnormalities including second degree (Type II) or third
             degree atrioventricular block. b) Cardiomyopathy, myocardial infarction, acute
             coronary syndromes (including unstable angina pectoris), coronary angioplasty,
             stenting, or bypass grafting within the past 6 months before enrollment. c) Congestive
             heart failure (Class II, III, or IV) as defined by the New York Heart Association
             (NYHA) functional classification system. d) Recent (within the past 6 months) history
             of symptomatic pericarditis.

          -  History of idiopathic pulmonary fibrosis, pneumonitis, interstitial lung disease, or
             organizing pneumonia, or evidence of active, non-infectious pneumonitis.

          -  Recent history (within 6 months) of uncontrolled symptomatic ascites or pleural
             effusions.

          -  Any serious and/or unstable pre-existing medical, psychiatric disorder, or other
             condition that could interfere with the subject's safety, obtaining informed consent,
             or compliance to the study procedures.

          -  Is or has an immediate family member (example, spouse, parent/legal guardian, sibling
             or child) who is investigational site or sponsor staff directly involved with this
             trial, unless prospective Institutional Review Board (IRB) approval (by chair or
             designee) is given allowing exception to this criterion for a specific subject.

          -  Prior treatment with the following agents: a) OX40, inducible T-cell co-stimulator
             (ICOS) agonist at any time. b) Prior systemic or intratumoral therapy with TLR
             agonist. c) Anticancer therapy or investigational therapy within 30 days or 5
             half-lives of the drug, whichever is shorter. d) Prior radiation therapy: permissible
             if at least 1 non-irradiated measurable lesion is available for assessment according
             to RECIST version 1.1 or if a solitary measurable lesion was irradiated, objective
             progression is documented. A wash out of at least 14 days before start of study
             treatment for radiation of any intended use to the extremities for bone metastases and
             28 days for radiation to the chest, brain, or visceral organs is required.

          -  Prior allogeneic or autologous bone marrow transplantation or other solid organ
             transplantation.

          -  Toxicity from previous treatment including: a) Toxicity Grade >=3 related to prior
             immunotherapy and that lead to study treatment discontinuation. b) Toxicity related to
             prior treatment has not resolved to Grade <=1 (except alopecia, or endocrinopathy
             managed with replacement therapy).

          -  Received transfusion of blood products (including platelets or red blood cells) or
             administration of colony stimulating factors (including granulocyte colony-stimulating
             factor [G-CSF], granulocyte macrophage colony-stimulating factor, and recombinant
             erythropoietin) within 2 weeks before the first dose of study treatment.

          -  Major surgery <=4 weeks before the first dose of study treatment. Subjects must have
             also fully recovered from any surgery (major or minor) and/or its complications before
             initiating study treatment.

          -  Known drug or alcohol abuse.

          -  Receipt of any live vaccine within 4 weeks.

        Additional Exclusion Criteria for Subjects in Part 2c

          -  Received prior anti-PD-1/PD-L1 therapy.