Inclusion Criteria: - Previously participated in prior clinical study CC-93538-EE-001 and either: - completed both the Induction and Maintenance phases; or - completed the Induction Phase, however, did not qualify for the Maintenance Phase, including having a severe eosinophilic esophagitis (EoE) flare requiring endoscopic intervention or rescue therapy. - Demonstrated compliance with required investigational product dosing during the prior study. - Did not permanently discontinue investigational product in the prior study and/or did not experience any clinically significant adverse events related to Investigational Product that would preclude further dosing. - 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 CC-93538-EE-001, 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 CC-93538-EE-001 are not eligible, 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 or ongoing infections including parasitic/helminthic infections, 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.