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Streaming systems evaluate massive workloads of event sequence aggregation queries. State-of-the-art approaches suffer from long delays caused by not sharing intermediate results of similar queries and by constructing event sequences prior to their aggregation. To overcome these limitations, our Shared Online Event Sequence Aggregation (Sharon) approach shares intermediate aggregates among multiple queries while avoiding the expensive construction of event sequences. Our Sharon optimizer faces two challenges. One, a sharing decision is not always beneficial. Two, a sharing decision may exclude other sharing opportunities. To guide our Sharon optimizer, we compactly encode sharing candidates, their benefits, and conflicts among candidates into the Sharon graph. Based on the graph, we map our problem of finding an optimal sharing plan to the Maximum Weight Independent Set (MWIS) problem. We then use the guaranteed weight of a greedy algorithm for the MWIS problem to prune the search of our sharing plan finder without sacrificing its optimality. The Sharon optimizer is shown to produce sharing plans that achieve up to an 18-fold speed-up compared to state-of-the-art approaches.