A session-based recommender system (SBRS) suggests the next item by modeling the dependencies between items in a session. Most of existing SBRSs assume the items inside a session are associated with one (implicit) purpose. However, this may not always be true in reality, and a session may often consist of multiple subsets of items for different purposes (e.g., breakfast and decoration). Specifically, items (e.g., bread and milk) in a subsethave strong purpose-specific dependencies whereas items (e.g., bread and vase) from different subsets have much weaker or even no dependencies due to the difference of purposes. Therefore, we propose a mixture-channel model to accommodate the multi-purpose item subsets for more precisely representing a session. Filling gaps in existing SBRSs, this model recommends more diverse items to satisfy different purposes. Accordingly, we design effective mixture-channel purpose routing networks (MCPRN) with a purpose routing network to detect the purposes of each item and assign it into the corresponding channels. Moreover, a purpose specific recurrent network is devised to model the dependencies between items within each channel for a specific purpose. The experimental results show the superiority of MCPRN over the state-of-the-art methods in terms of both recommendation accuracy and diversity.