Sequential recommendation is a task in which one models and uses sequential information about user behavior for recommendation purposes. We study sequential recommendation in a particularly challenging context, in which multiple individual users share asingle account (i.e., they have a shared account) and in which user behavior is available in multiple domains (i.e., recommendations are cross-domain). These two characteristics bring new challenges on top of those of the traditional sequential recommendation task. First, we need to identify the behavior associated with different users and different user roles under the same account in order to recommend the right item to the right user role at the right time. Second, we need to identify behavior in one domain that might be helpful to improve recommendations in other domains. In this work, we study shared account cross-domain sequential recommendation and propose Parallel Split-Join Network (PSJNet), a parallel modeling network to address the two challenges above. We present two variants of PSJNet, PSJNet-I and PSJNet-II. PSJNet-I is a "split-by-join" framework that splits the mixed representations to get role-specific representations and joins them to obtain cross-domain representations at each timestamp simultaneously. PSJNet-II is a "split-and-join" framework that first splits role-specific representations at each timestamp, and then the representations from all timestamps and all roles are joined to obtain cross-domain representations. We use two datasets to assess the effectiveness of PSJNet. Our experimental results demonstrate that PSJNet outperforms state-of-the-art sequential recommendation baselines in terms of MRR and Recall.