Multi-axis graphical modelling techniques allow us to perform network inference without making independence assumptions. This is done by replacing the independence assumption with a weaker assumption about the interaction between the axes; there are several choices for which assumption to use. In single-cell RNA sequencing data, genes may interact differently depending on whether they are expressed in the same cell, or in different cells. Unfortunately, current methods are not able to make this distinction. In this paper, we address this problem by introducing the strong product model for Gaussian graphical modelling.