Over many years, computational simulations based on Density Functional Theory (DFT) have been used extensively to study many different materials at the atomic scale. However, its application is restricted by system size, leaving a number of interesting systems without a high-accuracy quantum description. In this work, we calculate the electronic and structural properties of a graphene-metal system significantly larger than in previous plane-wave calculations with the same accuracy. For this task we use a localised basis set with the textsc{Conquest} code, both in their primitive, pseudo-atomic orbital form, and using a recent multi-site approach. This multi-site scheme allows us to maintain accuracy while saving computational time and memory requirements, even in our exemplar complex system of graphene grown on Rh(111) with and without intercalated atomic oxygen. This system offers a rich scenario that will serve as a benchmark, demonstrating that highly accurate simulations in cells with over 3000 atoms are feasible with modest computational resources.