Parallel Trajectory Splicing (ParSplice) allows for the efficient timewise parallelization of molecular dynamics-based simulations. The computational efficiency of ParSplice stems from the fact that parallel load-balancing is naturally optimized within the underlying algorithm. For this reason, ParSplice is a central component of the Exascale Atomistics for Accuracy, Length and Time (EXAALT) framework, being developed under the DOE Exascale Computing Project (ECP). Unfortunately, like most accelerated molecular dynamics techniques, a basic ParSplice implementation does not scale well with a growing system size, because global state-to-state transitions become much too frequent. Here, we demonstrate that the spatial scaling can be significantly improved when the system of interest is spatially decomposed into a sub-lattice structure. We will discuss the details of the Sub-lattice ParSplice method, as it has been implemented in EXAALT, and we will share some preliminary results.