Rise of the Runelords
Every 4th level, when you would usually raise a single ability by one, instead raise two distinct abilities by one. This allows for a bit more flexibility.
Once per session, you can use your Mulligan to be retroactively more clever. You can ret-con one action, either to have done something, or to erase an action (within reason). This gives people an option to address tactical errors (I totally used my move action to move here so you can get flank), preparatory (I had meant to cast resist energy, as we knew we were passing through a pit of fire), or just sensible (last night, before we dumped those bodies, we broke their jaws to prevent speak with dead).
Obviously, once an action is taken in response to a circumstance, it is no longer possible to Mulligan it away. You cannot Mulligan not leaving your mounts unattended after finding them eaten by wolves. The Mulligan is designed to help you with things your character is less likely to miss, not as a way to respond to a previous situation with new information.
The other use of a Mulligan is to correct errors. If you forgot that the spell you had up increased your damage by two, and your action has already passed, you may use a Mulligan to ret-con the effect.
Each player (and the DM) gets their own Mulligan each session. If something is sufficiently obvious to the character (I forgot I was bleeding to death, and failed to heal despite having the time and resources at my disposal), it will likely not require a use of your Mulligan, at DM discretion. A Mulligan is not required for something left unspecified, but logical (I had my weapon out as we walked down the corridor), but may be required if it is something out of the ordinary.
Over the course of playing, you will earn luck points. Luck points can be spent to increase any d20 roll you just made by rolling 1d6 and adding it to the result. You can add a luck roll after rolling the d20, but only before I tell you whether it was a success or not. You gain up to three luck points at the end of each session for roleplaying your beliefs (see above). You can only have five luck points at any given time.
At the end of each session, I will give you the opportunity to provide feedback. Let me know one thing you liked about that session and one thing you didn’t like. These two responses will each earn you a luck point. This is an effort to improve my DMing ability, so I will take your responses seriously.
The Banana Sticker
Any time another player does something you feel is worthy of special recognition, you can give them a banana sticker. For example, this can be sticking to your character’s values, undergoing some sort of personal change, or simply roleplaying a particular situation well. Each player can give one banana sticker per session, and the DM can give out or veto as many as he sees fit (this is to prevent abuse of the system, not to punish you, I want this to be fun!). Accumulated banana stickers will not only be a badge of pride and honour, but will also translate into a tangible, in-game reward: for each banana sticker you earn, gain a luck point. These luck points are separate from your regular pool—banana luck is extra fancy.