Aggregate Continuous Queries (ACQs) are among the most common Continuous Queries across all classes of monitoring applications and typically have a high execution cost. As such, optimizing the processing of ACQs is imperative for Data Stream Management Systems to reach their full potential. Existing multiple ACQs optimization schemes focus on ACQs with varying window specifications and pre-aggregation filters and 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 TriOps, that minimizes the repetition of operations at the sub-aggregation level, and a new multiple ACQs optimizer, called TriWeave, that is TriOps-aware. We analytically and experimentally demonstrate the performance gains of our proposed schemes, showing their superiority over alternative schemes. Finally, we generalize TriWeave to incorporate the classical subsumption-based multiquery optimization techniques for handling overlapping group-by attributes.