Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers; however exact methods are known to be inherently serial. We introduce an operator splitting implementation for irregular grids with a novel method to improve accuracy, and demonstrate potential for scalable parallel simulations in an initial MPI version. We foresee that this groundwork will enable larger scale, whole-cell stochastic simulations in the near future.