A Study to Assess the Adverse Events, Change in Disease Activity, and How Oral ABBV-711 Tablets Move Through the Body as a Monotherapy and in Combination With Intravenously Infused Budigalimab (ABBV-181), in Adults With Advanced Squamous Tumors

* Must have progressed on or after standard of care therapy and have no curative therapy available (participants who have refused, are considered ineligible for or are intolerant to standard of care therapy are eligible). * Received programmed cell death protein 1 (PD-1)/programmed cell death ligand 1 (PD-L1) targeted agents are eligible. * Confirmation of available archival tumor tissue (formalin-fixed paraffin-embedded \[FFPE\] block or freshly cut slides) or provision of fresh tissue biopsy is required for enrollment in this study for gene expression assessment. If archival tissue requirements cannot be met then the AbbVie therapeutic area Medical Director or designee should be contacted to determine subject eligibility. * For head and neck squamous cell carcinoma (HNSCC) participants enrolled in backfill (Part 1 and 3), subjects must provide consent to paired biopsies which are pretreatment and on treatment fresh tumor biopsies from the same tumor lesion, unless deemed not feasible by the investigator where upon consultation with the Sponsor is required. Paired biopsies are encouraged (when safe and feasible) but not required for subjects with squamous non-small cell lung cancer (sqNSCLC) enrolled in the backfill (Part 1 and 3). * Evaluable and measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) Version 1.1.

* Active autoimmune diseases besides vitiligo, type 1 diabetes, hypothyroidism, hypopituitarism and psoriasis (not requiring systemic treatment); history of primary immunodeficiency, bone marrow transplantation, or solid organ transplantation. Active inflammatory bowel disease unfit for trial in the opinion of the investigator, including subjects requiring systemic therapy with biologics or immunosuppressive therapy within the past 2 years. * Treatment with any of the following: * Anti-cancer therapy including chemotherapy, radiation therapy, immunotherapy, biologic, or any investigational therapy within 28 days or 5 half-lives of the drug (whichever is shorter) prior to the first dose of ABBV-711. Palliative radiation therapy for bone, skin or symptomatic metastases with 10 fractions or less is not subject to a washout period. * Radiation therapy for central nervous system metastases within 14 days prior to first dose. * Subject has systemically used known moderate/strong inhibitors of cytochrome P450 3A (CYP)3A enzyme isoform subfamily within 14 days or 5 half-lives of the drug (whichever is shorter) prior to the first dose of study treatment. * Has systemically used known moderate/strong inducers of CYP3A within 14 days prior to the first dose of study treatment. * Requires treatment with known moderate or strong inhibitors or inducers of CYP3A from the first dose of study treatment and for the duration of the study. * Administration or consumption of any of the following within 3 days prior to first dose of study treatment and while on study treatment: grapefruit or grapefruit products, Seville oranges (including marmaladecontaining Seville oranges), and star fruit. * Current or prior use of immunosuppressive medication within 14 days prior to the first dose of the study treatment. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids or local steroid injections (e.g., intra-articular injection); * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication); * Systemic corticosteroids at doses not to exceed 10 mg/day of prednisone or equivalent.