Most common diseases are influenced by multiple gene interactions and interactions with the environment. Performing an exhaustive search to identify such interactions is computationally expensive and needs to address the multiple testing problem. A four-step framework is proposed for the efficient identification of n-Way interactions. Methods: The framework was applied on a Multiple Sclerosis dataset with 725 subjects and 147 tagging SNPs. The first two steps of the framework are quality control and feature selection. The next step uses clustering and binary encodes the features. The final step performs the n-Way interaction testing. Results: The feature space was reduced to 7 SNPs and using the proposed binary encoding, more 2-SNP and 3-SNP interactions were identified compared to using the initial encoding. Conclusions: The framework selects informative features and with the proposed binary encoding it is able to identify more n-way interactions by increasing the power of the statistical analysis.