A computational model is proposed to study lithium-graphite intercalation compounds in the framework of Monte Carlo simulations in the Gran Canonical Ensemble. The results suggest the existence of fractional stages between stages II and I, which are rarely found in most experimental electrochemical measurements. These fractional stages seem to be part of a more general intercalation mechanism suggested for other intercalation compounds. The thermodynamic information obtained from the simulations for these fractional states at room temperature is discussed in the context of experimental data. In addition, clear evidence was found for the existence of a new stage, supported by recent experimental measurements. (C) 2018 The Electrochemical Society.