This is a dose-escalation study designed to evaluate the safety, pharmacokinetics, and pharmacodynamics of ABBV-927, and to determine the maximum tolerated dose (MTD) or recommended Phase 2 dose (RPTD) for ABBV-927 when administered as monotherapy or as combination therapy with ABBV-181 in participants with advanced solid tumors.

Inclusion Criteria:

• Participant has an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1.
• Participants have adequate bone marrow, kidney and liver function.
• Participants with a history of chronic heart failure or significant cardiovascular disease must have an echocardiogram or multigated acquisition scan indicating left ventricular ejection fraction greater than or equal to 45% within 28 days prior to the first dose of study drug.
• Participants must have creatinine clearance greater than or equal to 50 mL/min as measured by 24-hour urine or estimated by the Cockcroft-Gault formula.
• Participants must have total bilirubin less than or equal to 1.5 times the upper limit of normal (ULN), and aspartate aminotransferase and alanine aminotransferase less than or equal to 2.5 times ULN.
• Participants in all monotherapy arms must have an advanced solid tumor that has progressed on standard therapies known to provide clinical benefit or the participants are intolerant to such therapies.
• Participants in all combination therapy arms must have recurrent or metastatic HNSCC or NSCLC and previously received platinum-based therapy and progressed either during or after anti-programmed death ligand 1 (PDL1)-based therapy. In addition, participants must have received only one prior immunotherapy.
• The Sponsor may decide to limit the specific tumor types selected or treatment settings for specific arms based on evidence gathered.

Exclusion Criteria:

• Participant must not have an active or prior documented autoimmune disease in the last 2 years.
• Participant must not have current or prior use of immunosuppressive medication within 14 days prior to the first dose (with certain exceptions).
• Participant must not have a history of primary immunodeficiency, bone marrow transplantation, chronic lymphocytic leukemia, solid organ transplantation, previous clinical diagnosis of tuberculosis, inflammatory bowel disease, interstitial lung disease, or immune-mediated pneumonitis.
• Participant must not have a history of clinically significant uncontrolled condition(s) including but not limited to the following: uncontrolled hypertension; symptomatic congestive heart failure; unstable angina pectoris or cardiac arrhythmia including atrial fibrillation.
• Participant must not have a history of coagulopathy or a platelet disorder associated with significant clinical risk of thromboembolic event in the judgement of the investigator, or major thromboembolic event within 6 months prior to the first dose of study treatment.
• Participant must not have a prior grade greater than or equal to 3 immune-mediated neurotoxicity or pneumonitis while receiving immunotherapy.
• Participant must not have a known uncontrolled malignancy of the central nervous system.
• Participants in all combination therapy arms must not have a history of exposure to an immunotherapy experiencing an immune-mediated adverse event that required permanent discontinuation of the immunotherapy.
• Female participants must not be pregnant, breastfeeding or considering becoming pregnant during the study or for at least 3 or 5 months (for monotherapy and combination therapy participants, respectively) after the last dose of study drug.
• Male participants must not be considering fathering a child or donating sperm during the study or for at least 3 or 5 months (for monotherapy and combination therapy participants, respectively) after the last dose of study drug.
• Participant is judged by the investigator to have evidence of hemolysis.
• For Japan only, participants with a history of interstitial lung disease (pneumonitis) or current interstitial lung disease (pneumonitis).