The final cluster expansion was trained on a total of 7215 unique DFT calculations after filtering out structures which relax to off-lattice configurations, and possess transition metals in oxidation states not included in the model. Oxidation states were assigned using calculated magnetic moments. The variable oxidation state of Mn was assigned using a Bayesien black-box optimization process . We employed the icet and trainstation software packages to train the cluster expansion . The fitting used a pair-cluster cutoff of 7.1 Å and a triplet-cluster cutoff of 4.8 Å (quadruplet clusters were found to make only a very minor contribution to the model performance for increased complexity, so were excluded, as has been noted in other high-component cluster expansion studies of lithium transition metal oxides ). The final model has a cross validation score of 9.95 meV. More information on the fitting procedure can be found in the supporting information.