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Aggregate Continuous Queries (ACQs) are both a very popular class of Continuous Queries (CQs) and also have a potentially high execution cost. As such, optimizing the processing of ACQs is imperative for Data Stream Management Systems (DSMSs) to reach their full potential in supporting (critical) monitoring applications. For multiple ACQs that vary in window specifications and pre-aggregation filters, existing multiple ACQs optimization schemes assume a processing model where each ACQ is computed as a final-aggregation of a sub-aggregation. In this paper, we propose a novel processing model for ACQs, called Tri Ops, with the goal of minimizing the repetition of operator execution at the sub-aggregation level. We also propose Tri Weave, a Tri Ops-aware multi-query optimizer. We analytically and experimentally demonstrate the performance gains of our proposed schemes which shows their superiority over alternative schemes. Finally, we generalize Tri Weave to incorporate the classical subsumption-based multi-query optimization techniques.