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Local community detection has attracted much research attention recently, and many methods have been proposed for the single local community detection that finds a community containing the given set of query nodes. However, nodes may belong to several communities in the network, and detecting all the communities for the query node set, termed as the multiple local community detection (MLCD), is more important as it could uncover more potential information. MLCD is also more challenging because when a query node belongs to multiple communities, it always locates in the complicated overlapping region and the marginal region of communities. Accordingly, detecting multiple communities for such nodes by applying seed expansion methods is insufficient. In this work, we address the MLCD based on higher-order structural importance (HoSI). First, to effectively estimate the influence of higher-order structures, we propose a new variant of random walk called Active Random Walk to measure the HoSI score between nodes. Then, we propose two new metrics to evaluate the HoSI score of a subgraph to a node and the HoSI score of a node, respectively. Based on the proposed metrics, we present a novel algorithm called HoSIM to detect multiple local communities for a single query node. HoSIM enforces a three-stage processing, namely subgraph sampling, core member identification, and local community detection. The key idea is utilizing HoSI to find and identify the core members of communities relevant to the query node and optimize the generated communities. Extensive experiments illustrate the effectiveness of HoSIM.