Quasi-classical trajectory studies have been performed for the collision of internally excited methane with water using an accurate methane-water potential based on a full-dimensional, permutationally invariant analytical representation of energies calculated at a high level of theory. The results suggest that most energy transfer takes place at impact parameters smaller than about 8 Bohr; collisions at higher impact parameters are mostly elastic. Overall, energy transfer is fairly facile, with values for and approaching almost 2% of the total excitation energy. A classical model previously developed for the collision of internally excited molecules with atoms (Houston, P. L.; Conte, R.; Bowman, J. M. J. Phys. Chem. A 2015, 119, 4695-4710) has been extended to cover collisions of internally excited molecules with other molecules. For high initial rotational levels, the agreement with the trajectory results is quite good (R-2 approximate to 0.9), whereas for low initial rotational levels it is only fair (R-2 approximate to 0.7). Both the model and the trajectories can be characterized by a four-dimensional joint probability distribution, P(J(1,f),Delta E-1,J(2,f),Delta E-2), where J(1,f) and J(2,f) are the final rotational levels of molecules 1 and 2 and Delta E-1 and Delta E-2 are the respective changes in internal energy. A strong anticorrelation between Delta E-1 and Delta E-2 is observed in both the model and trajectory results and can be explained by the model. There is evidence in the trajectory results for a small amount of V <-> V energy transfer from the water, which has low internal energy, to the methane, which has substantial internal energy. This observation suggests that V <-> V energy transfer in the other direction also occurs.