This is a recent idea that I have tossed on my mind that can change the gameplay for both the Renegade(s) and Deputies. The Renegade, if he wishes, can choose to kill the Sheriff before he kills off all the other players. If he personally is the one that kills the Sheriff, he becomes the new Sheriff, has the new health limit bonus and gains 1 health. His mission is of course to survive like the deceased sheriff's mission was. If he only damages the Sheriff and the Outlaws or something else like Dynamite kills the Sheriff, game over and the Outlaws win. So it is a very risky move on his part, but it can be a way for him to shift the balance of the game and do something different. Imagine if a Sheriff is getting blown away and he will not be able to fend off the outlaws before the Sheriff dies. He can now kill the Sheriff and resume this role, so the Outlaws don't immediately win. But he wouldn't want the Sheriff to be overwhelmed every time because if he did, then he has no Renegade of his own to back him, and so might get overpowered himself. Think of how stupid this would be on his part in a 4-player game. I think this is a fascinating change to the Renegade role. It might be worth specifying a certain amount of players that need to be killed before he can do this, but it could be good on its own too.
As for the deputies, I think there is two things that could happen here. One, they could have to defend the Renegade who has become the new Sheriff. I think a more interesting variant is that they were loyal to their old Sheriff and won't side with the new Sheriff. They become Renegades themselves! Now, they might have the opportunity to become the new Sheriff as well if they depose the prior Renegade, or it could be that only the original Renegade has the capacity. Anyway, I think this could be an interesting way to switch things up.