Thagard's theory of explanatory coherence (TEC) and its implementation ECHO might be considered as the de facto calculus of explanatory coherence. It is an elaborate framework to compare competing scientific theories. Recently, it has become apparent that TEC is also useful as a tool for the analysis of different scenarios in so-called sense-making systems. To this end, it is expedient to discuss a number of extensions and modifications to TEC. This article proposes a number of extensions and modifications to TEC in the context of sense-making systems. The following topics are discussed: input format, representation of false formulas, representation languages, relaxation methods, schemes of coherence, metaexplanations, scenarios, leaking hypotheses, knowledge acquisition, and contextual explanation. The discussion is detailed enough to carry through changes in existing sense-making systems.