Context. An extension method is a method declared in a package other than the package of its host class. Thanks to extension methods, developers can adapt to their needs classes they do not own: adding methods to core classes is a typical use case. This is particularly useful for adapting software and therefore to increase reusability. Inquiry. In most dynamically-typed languages, extension methods are globally visible. Because any developer can define extension methods for any class, naming conflicts occur: if two developers define an extension method with the same signature in the same class, only one extension method is visible and overwrites the other. Similarly, if two developers each define an extension method with the same name in a class hierarchy, one overrides the other. To avoid such “accidental overrides”, some dynamically-typed languages limit the visibility of an extension method to a particular scope. However, their semantics have not been fully described and compared. In addition, these solutions typically rely on a dedicated and slow method lookup algorithm to resolve conflicts at runtime. Approach. In this article, we present a formalization of the underlying models of Ruby refinements, Groovy categories, Classboxes, and Method Shelters that are scoping extension method solutions in dynamically-typed languages. Knowledge. Our formal framework allows us to objectively compare and analyze the shortcomings of the studied solutions and other different approaches such as MultiJava. In addition, language designers can use our formal framework to determine which mechanism has less risk of “accidental overrides”. Grounding. Our comparison and analysis of existing solutions is grounded because it is based on denotational semantics formalizations. Importance. Extension methods are widely used in programming languages that support them, especially dynamically-typed languages such as Pharo, Ruby or Python. However, without a carefully designed mechanism, this feature can cause insidious hidden bugs or can be voluntarily used to gain access to protected operations, violate encapsulation or break fundamental invariants.