Inclusion Criteria:  Ability to comprehend and willingness to sign a written ICF for the study. Male or female participant aged 18 years or older inclusive at the time of signing the ICF. Must be willing and able to conform to and comply with all Protocol requirements Willingness to undergo pre- and on-treatment tumor biopsy. Have CD8 T-cell-positive tumors ECOG performance status 0 or 1. Measurable disease according to RECIST v1.1. Participants with SCCHN: Participants with histologically or cytologically confirmed squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx, or larynx not amenable to local therapy with curative intent (surgery or radiation with or without chemotherapy). Participants with specified GI malignancies: Histologically or cytologically confirmed advanced or metastatic colorectal (CRC), gastric/gastroesophageal junction (GEJ) cancer, hepatocellular carcinoma (HCC), pancreatic ductal adenocarcinoma (PDAC), or squamous carcinoma of the anal canal (SCAC). Participants should have disease progression after treatment with available therapies, including anti-PD-(L)1 therapy (if applicable), that are known to confer clinical benefit or who are intolerant to or ineligible for standard treatment. Prior anti-PD-(L)1 therapy should not have been discontinued because of intolerance. For participants to be enrolled in cohorts including INCB106385: The ability to swallow oral medication. Willingness to avoid pregnancy or fathering children  Exclusion Criteria:  Clinically significant cardiac disease, unstable angina, acute myocardial infarction within 6 months of Cycle 1 Day 1, and New York Heart Association Class III or IV congestive heart failure. History or presence of an ECG abnormality that, in the investigator's opinion, is clinically meaningful. Known active CNS metastases and/or carcinomatous meningitis. Participants who have active or inactive autoimmune disease or syndrome (eg, rheumatoid arthritis, moderate or severe psoriasis, multiple sclerosis, inflammatory bowel disease) that has required systemic treatment in the past 2 years or who are receiving systemic therapy for an autoimmune or inflammatory disease (ie, with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (doses > 10 mg daily of prednisone or equivalent) or any other form of immunosuppressive therapy within 7 days before the first dose of study treatment. Known additional malignancy that is progressing or requires active treatment, or history of other malignancy within 2 years of the first dose of study treatment with the exception of cured basal cell or squamous cell carcinoma of the skin, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in situ of the cervix, or other noninvasive or indolent malignancy, or cancers from which the participant has been disease free > 1 year after treatment with curative intent. Participants with protocol specified exclusionary hematology, hepatic, renal and coagulation laboratory values at screening.  Has not recovered to ≤ Grade 1 from toxic effects of prior therapy (including prior immunotherapy) and/or complications from prior surgical intervention before starting study treatment.  Evidence of interstitial lung disease, history of interstitial lung disease, or active noninfectious pneumonitis. Immune-related toxicity during prior immune therapy for which permanent discontinuation of therapy is recommended, OR any immune-related toxicity requiring intensive or prolonged immunosuppression to manage. Prior treatment with any adenosine pathway targeting drugs. Any prior chemotherapy, biological therapy, or targeted therapy to treat the participant's disease within 5 half-lives or 28 days (whichever is shorter) before the first dose of study treatment. Any prior radiation therapy within 28 days before the first dose of study treatment. Undergoing treatment with another investigational medication or having been treated with an investigational medication within 5 half-lives or 28 days (whichever is shorter) before the first dose of study treatment. For participants to be enrolled in cohorts including INCB106385: concomitant treatment with strong CYP3A4 inhibitors or inducers. Receipt of a live virus vaccine within 30 days of the first dose of study treatment. Infection requiring parenteral antibiotics, antivirals, or antifungals within 1 week of the first dose of study treatment. Known or suspected SARS-CoV-2 infection at the time of enrollment. Active HBV or HCV infection that requires treatment. HBV-DNA and HCV-RNA must be undetectable. Participants who have cleared a prior HBV infection (defined as HBsAg negative, HBsAg antibody positive, and anti-HBc antibody positive) are eligible for the study. Known history of HIV (HIV 1/2 antibodies). History of organ transplant, including allogeneic stem-cell transplantation or CAR-T cell therapy. Known hypersensitivity or severe reaction to any component of study drug(s) or formulation components. For participants to be enrolled in cohorts including INCB106385: Inability to swallow food or any concomitant condition of the upper GI tract that precludes administration of oral medications. Is pregnant or breastfeeding. Any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study treatment and attending required study visits; pose a significant risk to the participant; or interfere with interpretation of study data. The following participants are excluded in France: vulnerable populations according to article L.1121-6 of the French Public Health Code and adults under legal protection or who are unable to express their consent per article L.1121-8 of the French Public Health Code.