Last year has witnessed the re-flourishment of tag-aware recommender systems supported by the LLM-enriched tags. Unfortunately, though large efforts have been made, current solutions may fail to describe the diversity and uncertainty inherent in user preferences with only tag-driven profiles. Recently, with the development of geometry-based techniques, e.g., box embeddings, the diversity of user preferences now could be fully modeled as the range within a box in high dimension space. However, defect still exists as these approaches are incapable of capturing high-order neighbor signals, i.e., semantic-rich multi-hop relations within the user-tag-item tripartite graph, which severely limits the effectiveness of user modeling. To deal with this challenge, in this paper, we propose a novel framework, called BoxGNN, to perform message aggregation via combinations of logical operations, thereby incorporating high-order signals. Specifically, we first embed users, items, and tags as hyper-boxes rather than simple points in the representation space, and define two logical operations, i.e., union and intersection, to facilitate the subsequent process. Next, we perform the message aggregation mechanism via the combination of logical operations, to obtain the corresponding high-order box representations. Finally, we adopt a volume-based learning objective with Gumbel smoothing techniques to refine the representation of boxes. Extensive experiments on two publicly available datasets and one LLM-enhanced e-commerce dataset have validated the superiority of BoxGNN compared with various state-of-the-art baselines. The code is released online: https://github.com/critical88/BoxGNN.