This is an open-label, Phase 1, dose-escalation study to determine the maximum tolerated dose (MTD) and the recommended phase two dose (RPTD), and to assess the safety, preliminary efficacy, and pharmacokinetic (PK) profile of ABBV-321 for participants with advanced solid tumors likely to overexpress the epidermal growth factor receptor (EGFR). The study will consist of 2 phases: Dose Escalation Phase and Expansion Phase.

Inclusion Criteria:

• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
• Histologically or cytologically confirmed solid tumor of one of the following types associated with overexpression of Epidermal Growth Factor Receptor (EGFR). (For Expansion Phase: Subjects must have EGFR overexpression demonstrated by central assessment or Sponsor selected test).

Dose Escalation Phase:

• Colorectal cancer (CRC), Glioblastoma (GBM), squamous cell carcinoma of the head and neck (HNSCC), non-small cell lung cancer (NSCLC), bladder, cervical, esophageal, kidney or sarcoma.
• Participants must have disease that has progressed on prior treatment and is not amenable to surgical resection or other approved therapeutic options with curative intent. Participants must not be eligible for, or has refused further therapy that is likely to provide a survival benefit.
• Must have measureable disease as per RECIST Version 1.1 or RANO (for GBM).
• Minimum life expectancy of at least 12 weeks.

Expansion Phase (Solid Tumor Cohort):

• Histologically or cytologically confirmed advanced solid tumor.
• Participants must have disease that has progressed on prior treatment and is not amenable to surgical resection or other approved therapeutic options with curative intent.
• Must have measureable disease as per RECIST Version 1.1.
• Minimum life expectancy of at least 12 weeks.

Expansion Phase (GBM Cohort Only):

• Participant has recurrent primary (de novo) glioblastoma histologically confirmed at any time from initial diagnosis through latest recurrence.
• Participant has recurrent GBM per Response Evaluation in Neuro-Oncology (RANO) requirements.
• Tumor is measurable according to RANO criteria.

Exclusion Criteria:

• Active uncontrolled infection National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE Grade greater than or equal to 3).
• New York Heart Association (NYHA) Class III or IV heart failure and/or ejection fraction of < 40% as measured by echocardiogram at screening.
• Unstable angina pectoris or cardiac ventricular arrhythmia.
• Myocardial infarction or cerebrovascular accident (CVA) within 6 months.
• Documented history of capillary leak syndrome within 6 months of study enrollment.
• Grade 2 or higher peripheral edema, ascites, pleural, or pericardial effusion within 4 weeks of study enrollment or any history of recurrent grade 2 or higher effusions requiring ongoing drainage.
• Active keratitis or current corneal disorder.
• Laser-assisted in situ keratomileusis (LASIK) procedure within the last 1 year or cataract surgery within the last 3 months.
• Major surgery (including opening of the abdomen, chest) within 21 days of the first dose of study drug.
• Uncontrolled metastases from an extracranial solid tumor to the central nervous system (CNS). Participants with brain metastases from an extracranial solid tumor are eligible after definitive therapy provided they are asymptomatic for at least 2 weeks prior to first dose of ABBV-321.
• No history of medical condition resulting in nephrotic range proteinuria.
• Participants must not have been treated in anticancer therapy including chemotherapy, immunotherapy, radiotherapy, hormonal therapy, biologic therapy or investigational anti-cancer therapy within a period of 21 days or herbal anticancer therapy within 7 days prior to the first dose of study drug.
• For approved targeted small molecules, a washout period of 5 half-lives is adequate (no washout period required for subjects currently on erlotinib)
• Participant must not have been in more than three lines of systemic cytotoxic therapy (excluding adjuvant and neoadjuvant therapy)