Cross sections for the collision of a highly excited atom with a polar molecule have been calculated using a classical trajectory Monte-Carlo approach. Many features of experiment have been observed and explained. For example, the tendency for the Rydberg atom to be further excited can be explained by the likelihood for multiple electron-molecule encounters. Furthermore, the probability of multiple encounters also casts doubts on the validity of the free electron model, a commonly used approach in Rydberg collision problems. Quantitatively, the state changing cross sections calculated in this study are typically smaller than experimental measurements. This may be due to the failure of classical mechanics to quantize the possible states of a physical system, especially since the total cross section agrees with experiment. It is thus hoped that a proposed semi-classical procedure, in which the molecule is treated quantum mechanically, will produce results in better agreement with experiment.