SNOMED CT is a large-scale medical ontology which is developed using a variant of the inexpressive Description Logic ℰℒ, a logic-based knowledge representation formalism and a logical underpinning of OWL 2 EL Profile. Description Logic reasoning can be used to compute subsumption relationships between SNOMED CT concepts and to pinpoint the reasons why a certain subsumption holds by finding justifications (sets of axioms responsible for this relationship). This helps the ontology developers to understand such a relationship and to debug it if needed. This article describes an extension of the method of finding one justification to one that finds all justifications for a given subsumption, introduces a SNOMED CT-specific optimization, and presents empirical evaluation results. Our extensive experiments on SNOMED CT show that (i) the proposed modularization-based approach makes it practicable to find all justifications in most cases in SNOMED CT; (ii) the first ten justifications, if any, for a subsumption can be computed in an acceptable runtime, and can be displayed in an incremental manner, i.e., the ontology developers may inspect the first justification while the reasoner continues to find more; and (iii) there is a high degree of commonality among justifications for a subsumption of interest.