This study proposes a method of in-network aggregate query processing to reduce the number of messages incurred in a wireless sensor network. When aggregate queries are issued to the resource-constrained wireless sensor network, it is important to efficiently perform these queries. Given a set of multiple aggregate queries, the proposed approach shares intermediate results among queries to reduce the number of messages. When the sink receives multiple queries, it should be propagated these queries to a wireless sensor network via existing routing protocols. The sink could obtain the corresponding topology of queries and views each query as a query tree. With a set of query trees collected at the sink, it is necessary to determine a set of backbones that share intermediate results with other query trees (called non-backbones). First, it is necessary to formulate the objective cost function for backbones and non-backbones. Using this objective cost function, it is possible to derive a reduction graph that reveals possible cases of sharing intermediate results among query trees. Using the reduction graph, this study first proposes a heuristic algorithm BM (standing for Backbone Mapping). This study also develops algorithm OOB (standing for Obtaining Optimal Backbones) that exploits a branch-and-bound strategy to obtain the optimal solution efficiently. This study tests the performance of these algorithms on both synthesis and real datasets. Experimental results show that by sharing the intermediate results, the BM and OOB algorithms significantly reduce the total number of messages incurred by multiple aggregate queries, thereby extending the lifetime of sensor networks.