Metonymy resolution (MR) is a challenging task in the field of natural language processing. The task of MR aims to identify the metonymic usage of a word that employs an entity name to refer to another target entity. Recent BERT-based methods yield state-of-the-art performances. However, they neither make full use of the entity information nor explicitly consider syntactic structure. In contrast, in this paper, we argue that the metonymic process should be completed in a collaborative manner, relying on both lexical semantics and syntactic structure (syntax). This paper proposes a novel approach to enhancing BERT-based MR models with hard and soft syntactic constraints by using different types of convolutional neural networks to model dependency parse trees. Experimental results on benchmark datasets (e.g., ReLocaR, SemEval 2007 and WiMCor) confirm that leveraging syntactic information into fine pre-trained language models benefits MR tasks.