The capacity region of the interference channel with common messages is studied. This channel model is a variation of the classical two user interference channel modified such that each encoder has both a private message as well as a common message to be decoded at both receivers. Achievable rates for this channel model can be characterized by the classical Han-Kobayashi achievable rate region for the interference channel in which, at each encoder, the codeword embedding the private message is superimposed over the codeword for the common message. We show that the achievable rates for this region can be improved upon by rate-sharing, which consist of transmitting part of the private message into the common codeword. This improved region is shown to approach the capacity for a class of injective semi-deterministic channels. Moreover, we show that the Fourier Motzkin elimination of the Han-Kobayashi with rate-sharing contains less rate bounds than the one without rate-sharing. This approach provides an alternative proof of the simplification of the Han-Kobayashi originally shown by Chong et al. This result is particularly interesting as it shows that simplifications in the spirit of Chong et al. for general channels can be performed through rate-sharing and Fourier-Motzkin elimination. This approach can be easily implemented algorithmically and is relevant in the context of the automatic derivation of achievable rate regions.