Web service composition composes existing web services to accommodate users’ requests for required functionalities with the best possible quality of services (QoS). Due to the computational complexity of this problem, evolutionary computation (EC) techniques have been employed to efficiently find composite services with near-optimal functional quality (i.e., quality of semantic matchmaking, QoSM for short) or non-functional quality (i.e., QoS) for each composition request individually. With a rapid increase in composition requests from a growing number of users, solving one composition request at a time can hardly meet the efficiency target anymore. Driven by the idea that the solutions obtained from solving one request can be highly useful for tackling other related requests, multitasking service composition approaches have been proposed to efficiently deal with multiple composition requests concurrently. However, existing attempts have not been effective in learning and sharing knowledge among solutions for multiple requests. In this paper, we model the problem of collectively handling multiple service composition requests as a new multi-tasking service composition problem and propose a new Permutation-based Multi-factorial Evolutionary Algorithm based on an Estimation of Distribution Algorithm (EDA), named PMFEA-EDA, to effectively and efficiently solve this problem. In particular, we introduce a novel method for effective knowledge sharing across different service composition requests. For that, we develop a new sampling mechanism to increase the chance of identifying high-quality service compositions in both the single-tasking and multitasking contexts. Our experiment shows that our proposed approach, PMFEA-EDA, takes much less time than existing approaches that process each service request separately, and also outperforms them in terms of both QoSM and QoS.