Abstract Our interactions with an application frequently leave a heterogeneous and contemporaneous trail of actions and adoptions (e.g., clicks, bookmarks, purchases). Given a sequence of a particular type (e.g., purchases)– referred to as the target sequence, we seek to predict the next item expected to appear beyond this sequence. This task is known as next-item recommendation. We hypothesize two means for improvement. First, within each time step, a user may interact with multiple items (a basket), with potential latent associations among them. Second, predicting the next item in the target sequence may be helped by also learning from another supporting sequence (e.g., clicks). We develop three twin network structures modeling the generation of both target and support basket sequences. One based on “Siamese networks” facilitates full sharing of parameters between the two sequence types. The other two based on “fraternal networks” facilitate partial sharing of parameters. Experiments on realworld datasets show significant improvements upon baselines relying on one sequence type.