Levi Kornelsen wrote a post about using rpg rules as a toy when playing. I find the idea intriguing, having done something similar as a gamemaster of several homebrew games.
The idea is that playing with the rules (as opposed to by the rules) is part of the fun: Assume a game does not have mass combat system. A large combat occurs with a player character leading one side. How to handle it? Or maybe the game doesn’t have good rules for climbing on a dragon and stabbing it to death while riding it. Or whatever.
My gut reaction is that d20 would be particularly suited for this kind of play, because it has many moving parts. Climbing on a dragon and then scewering it could mean bypassing natural armour, getting automatic critical threats (for a particularly weak spot), doing it extra con damage, having it treated as flat-footed against your char, or a myriad of other possibilities.
Combine this idea with Ryan Stoughton’s little pdf named Raising the Stakes (direct link), which is a free download on the E6-wiki. The relevant part of the PDF is that players can suggest extra effects for their rolls, but they also have to suggest the heightened negative consequences for failing the roll. GM can accept or decline the suggestion. Like: “I raise the dragon being flat-footed against me falling prone right next to it”, in context of aforementioned climbing. GM accepts or declines.
This will not work when some participants are not familiar enough with the rules. Further, a common standard for the kind of fiction to create is necessary: If some players are going for extremely gritty style and others high-action anime combats, there will be some disagreements ahead (this is true in general, but even more so in case where this variant is used).
It would be possible to even build a little d20 variant around this. Say, generic classes that get one ability/feat/whatever per level. Stunts would work as per raising stakes above, the feats/class abilities would be essentially stunts the character has mastered (and can use at will without explicit GM permission).