A Study to Evaluate the Safety and Effectiveness of ILIxadencel Administered Into Tumors in Combination With Checkpoint Inhibitor (CPI) in Patients With ADvanced Cancer

Inclusion Criteria: * Must provide written informed consent. * Must have histologically confirmed and specific (Human Papilloma Virus) HPV-positive or HPV-negative squamous cell carcinoma of the head and neck (SCCHN), non-small-cell lung cancer (NSCLC) or gastric or gastroesophageal junction (GEJ) adenocarcinoma. Patients with other tumor types who are candidates for pembrolizumab therapy (according to the FDA-approved prescribing information at the time of inclusion) can also be enrolled in Phase 1b. Tumor histology and most recent pathology report must be in subject's medical record. Tumor samples and/or biopsies will not be collected as part of this study. * Eligible for pembrolizumab treatment per country-specific label and per physician's decision. * ECOG (Eastern Cooperative Oncology Group) performance status of 0 or 1. * Adequate organ function. * Women of childbearing potential must follow contraceptive requirements; must have a negative pregnancy blood test at screening, and a negative blood or urine pregnancy test within 24 hours before each dose of ilixadencel; and must not be breastfeeding. * Male subjects must agree to use condoms from screening until 90 days after the last dose of ilixadencel, or must have a female partner using a highly effective method of contraception as described above. Exclusion Criteria: * Prior history of invasive malignancy, unless complete remission has been achieved for at least 3 years and no additional therapy is required except for hormonal therapy or bisphosphonates. * Active or previously untreated brain and/or leptomeningeal metastasis. * Active autoimmune disease, pneumonitis or interstitial lung disease. * Certain heart conditions including, but not limited to: Congestive heart failure; uncontrolled hypertension; unstable angina pectoris; pericarditis; myocarditis; mycardial infarction 6 months prior to study. * Systemic immunosuppression except for replacement therapy. * Life expectancy of less than 3 months. * Any prior treatment with ilixadencel or prior treatment with anticancer agents (except pembrolizumab or other CPI for subjects in Phase 1b) within 4 weeks of starting study medication. * Major surgery or significant traumatic injury within 4 weeks before study start. * Known infection with human immunodeficiency virus (HIV). * Active tuberculosis; active infection requiring anti-infective therapy (hepatitis with a negative viral load on maintenance will not be excluded). Other protocol-defined inclusion/exclusion criteria could apply.