Parallel production lines are a design option often used in chemical batch plants. In recent research, this option has been introduced into the strategic multiproduct batch plant design problem, assuming a single product campaign mode of operation. However, to accommodate for other modes of operation and different production strategies, more explicit scheduling should be considered. In this paper, the combined design and scheduling optimization of multiple lines multistage plants is addressed. More specifically, we explored the Resource-Task Network formulation, in which constraints were included to exploit the sequential characteristics of the problem under study. Furthermore, two solution approaches were studied: a general holistic one and, triggered by the rapid increase in problem size and computational expense, a decomposition approach. In this decomposition approach, the problem is divided into smaller subproblems, by fixing the number of lines, which are iteratively solved. The performance of both approaches are compared via several illustrative examples.