As stream data is being more frequently collected and analyzed, stream processing systems are faced with more design challenges. One challenge is to perform continuous window aggregation, which involves intensive computation. When there are a large number of aggregation queries, the system may suffer from scalability problems. The queries are usually similar and only differ in window specifications. In this paper, we propose collaborative aggregation which promotes aggregate sharing among the windows so that repeated aggregate operations can be avoided. Different from the previous approaches in which the aggregate sharing is restricted by the window pace, we generalize the aggregation over multiple values as a series of reductions. Therefore, the results generated by each reduction step can be shared. The sharing process is formalized in the feed semantics and we present the compose-and-declare framework to determine the data sharing logic at a very low cost. Experimental results show that our approach offers an order of magnitude performance improvement to the state-of-the-art results and has a small memory footprint.