Inclusion Criteria: - Previously participated in prior clinical study CC-93538-EE-001 and either: 1. Subject experienced a severe EoE flare requiring endoscopic intervention and/or concomitant rescue therapy during the Induction Phase and has completed Week 24 of the Induction Phase; OR 2. Subject completed the Induction Phase and does not qualify for entry to the Maintenance Phase for reasons other than a severe EoE flare; OR 3. Subject experienced a severe EoE flare requiring endoscopic intervention and/or concomitant rescue therapy during the Maintenance Phase and completed Week 48 of the Maintenance Phase; OR 4. Subject completed Week 48 of the Maintenance Phase - OR Subject must have participated in Study CC-93538-DDI-001 and completed assessments through the end of treatment visit - Demonstrated ≥ 80% and ≤ 120% overall compliance with required investigational product dosing during the prior studies. - Did not permanently discontinue investigational product in the prior studies and/or did not experience any clinically significant adverse events related to Investigational Product that would preclude further dosing in the opinion of the Investigator. - Females of childbearing potential must have a negative pregnancy test prior to the first dose of open-label CC-93538 and agree to practice a highly effective method of contraception (as defined in the prior study) until 5 months after the last dose of open-label CC-93538. Exclusion Criteria: - Clinical or endoscopic evidence of other diseases or conditions that may affect or confound the histologic, endoscopic, or clinical symptom evaluation for this study. - Active Helicobacter pylori infection or esophageal varices. - Evidence of immunosuppression, or of having received systemic immunosuppressive or immunomodulating drugs within 5 drug half-lives prior to open-label extension study (OLE) Day 1. Use of these agents is prohibited during the study. - Treatment with oral or sublingual immunotherapy within 6 months of OLE Day 1. Use of these agents is prohibited during the study. - Received an investigational product, other than that administered in the CC-93538-EE-001 or CC-93538-DDI-001 studies, within 5 half-lives prior to OLE Day 1 (includes investigational product received during an interventional trial for COVID-19). Those vaccinated with an investigational COVID-19 vaccine during the CC-93538-EE-001 or CC-93538-DDI-001 studies are not eligible to participate, unless allowed following a discussion with the Clinical Trial Physician. - Received a live attenuated vaccine within one month prior to OLE Day 1; or anticipates the need for a live attenuated vaccine at any time throughout the course of this study. - Any disease that would affect the conduct of the protocol or interpretation of the study results, or would put a patient at risk by participating in the study (e.g. colitis, celiac disease, Mendelian disorder associated with EoE, severe uncontrolled asthma, infection causing eosinophilia, hypereosinophilic syndrome, or cardiovascular condition, or neurologic or psychiatric illness that could compromise the participant's ability to accurately document symptoms of EoE; newly diagnosed malignancy, lymphoproliferative disease, or clinically significant laboratory abnormality). - Active parasitic/helminthic infection or a suspected parasitic/helminthic infections or chronic infection (viral hepatitis, tuberculosis, or HIV) - Has had idiopathic anaphylaxis or major immunologic reaction to an immunoglobulin-G containing agent; or any known hypersensitivity to any ingredient in CC-93538. - Females who are pregnant or lactating.