Oliveira and colleagues recently developed a powerful model to reason about mixin-based composition of effectful components and their interference, exploiting a wide variety of techniques such as equational reasoning, parametricity, and algebraic laws about monadic effects. This work addresses the issue of reasoning about interference with effectful aspects in the presence of unrestricted quantification through pointcuts. While global reasoning isrequired, we show that it is possible to reason in a compositional manner, which is key for the scalability of the approach in the face of large and evolving systems. We establish a general equivalence theorem that is based on a few conditions that can be established, reused, and adapted separately as the system evolves. Interestingly, one of these conditions, local harmlessness, can be proven by a translation to the mixin setting, making it possible to directly exploit previously established results about certain kinds of harmless extensions.