Mastering a foreign language like English can bring better opportunities. In this context, although multiword expressions (MWE) are associated with proficiency, they are usually neglected in the works of automatic scoring language learners. Therefore, we study MWE-based features (i.e., occurrence and concreteness) in this work, aiming at assessing their relevance for automated essay scoring. To achieve this goal, we also compare MWE features with other classic features, such as length-based, graded resource, orthographic neighbors, part-of-speech, morphology, dependency relations, verb tense, language development, and coherence. Although the results indicate that classic features are more significant than MWE for automatic scoring, we observed encouraging results when looking at the MWE concreteness through the levels.