We propose a unified framework that enables us to consider various aspects of contextualization at different levels to better identify the idiomaticity of multi-word expressions. Through extensive experiments, we demonstrate that our approach based on the inter- and inner-sentence context of a target MWE is effective in improving the performance of related models. We also share our experience in detail on the task of SemEval-2022 Tasks 2 such that future work on the same task can be benefited from this.