Analytical queries virtually always involve aggregation and statistics. SQL offers a wide range of functionalities to summarize data such as associative aggregates, distinct aggregates, ordered-set aggregates, grouping sets, and window functions. In this work, we propose a unified framework for advanced statistics that composes all flavors of complex SQL aggregates from low-level plan operators. These operators can reuse materialized intermediate results, which decouples monolithic aggregation logic and speeds up complex multi-expression queries. The contribution is therefore twofold: our framework modularizes aggregate implementations, and outperforms traditional systems whenever multiple aggregates are combined. We integrated our approach into the high-performance database system Umbra and experimentally show that we compute complex aggregates faster than the state-of-the-art HyPer system.