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Multi-trait Essay Scoring (MES) aims to evaluate the quality of essays across multiple traits (e.g., Language, Content, and Organization). The task can be summarized into three crucial steps: essay content encoding, trait feature learning, and multi-trait scoring. However, previous methods fall short in these steps due to neglecting essential scoring-oriented knowledge, leading to suboptimal performance. To track these issues, we propose a novel multi-trait scoring framework with multi-knowledge enhancement. Specifically, linguistic knowledge is used to model syntactic structural relations between words, highlighting structurally-informed essay encoding. We learn trait knowledge by capturing the knowledge dependencies between traits to enhance trait-specific features. Further, score-aware ordinal knowledge is integrated to promote ordinal alignment in trait-specific features associated with score rankings, improving scoring performance. Extensive experiments show that our proposed method achieves significant performance.