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In this paper, we build upon previous work that aims at recuperating aspect oriented ideas into component based software development. In that research, a composition adapter was proposed in order to capture crosscutting concerns in the PacoSuite component based methodology. A composition adapter is visually applied onto a given component composition and the changes it describes are automatically applied. Stacking multiple composition adapters onto the same component composition can however lead to unpredictable and undesired side-effects. In this paper, we propose a solution for this issue, widely known as the feature interaction problem. We present a classification of different interaction levels among composition adapters and the algorithms required to verify them. The proposed algorithms are however of exponential nature and depend on both the composition adapters and the component composition as a whole. In order to enhance the performance of our feature interaction analysis, we present a set of theorems that define the interaction levels solely in terms of the properties of the composition adapters themselves.