It should come as no surprise that I'm quite fond of fudge dice, and I've put a lot of thought into the different things that can be done with their three outcomes. I've shifted things on several different axes, and I've failed as often as I've succeeded, but it's a fun area to play in.
One idea that I'm quite fond of is less about altering the dice or how they're rolled and more about what that mean. Specifically, you can get a lot of mileage out of separating the dice from the outcome.
To illustrate what that means, consider that on a normal df roll, you are judging an outcome, generally based on die roll plus whatever skill is in use as well as any other bonuses or penalties. The final outcome is expressed as a number or an adjective (or both) and that's what's used as a basis for narration.
Now, as gamers we have always implicitly understood that there can be some separation between the dice and the outcome, specifically in situations where the dice roll badly but the roll is a success or vice versa. What I propose here is to make the distinction a little bit more explicit, and make the roll itself as important to the narration as the outcome.
To do this requires a little thought about what the die roll means. Most often, we think of it as representing the role of luck in an activity, but that doesn't hold up under any real scrutiny. Luck maybe part of our lives, but it's usually something we consider as part of what happens to us, less about what we do. If we miss a target, it's because we need to get _better_, not luckier.
So instead, consider the dice to represent all the other factors that the system hasn't already accounted for. Distractions, coincidences, a good nights sleep and anything else. Think of all the reasons you succeed and fail and - unless you're a terrible egoist - those external factors will become obvious.
With that in mind, the dice represent the "swing" of the world at large. For narrow results (-1 to +1) nothing of any real note happened. You tried, you succeeded or failed, that's just the way things go.
For slightly broader results (-2 or +2) something went right or wrong. Someone gave you directions. The wind was at your back. The wind _wasn't_ at your back. The lighting was off. THere's something you can point to and say "That helped" or "Man, that got in my way".
Rarer results (-3 or +3) represent rare strokes of luck or bad luck. Coincidence falls for or against you. The librarian just happens to be and expert on the topic in question. The supplies you need were destroyed in a freak fire. Your opponent slipped on a patch of oil. You take a nail in one of your tires.
By this thinking, critical results (-4 or +4) are just a logical extension of this model. They're the truly preposterous strokes of luck, good and bad, that turn a situation around.
With this in mind, you can combine this information with the outcome (which won't be changed) to be able to describe action in terms of "success because" or even "success in spite of" to get a better picture of how a given even transpired.
This combines interestingly with aspects. If you do a dice-flipping bonus (that is, invoke to turn a die to a +) then you need to describe how the aspect is changing the situation, maybe turning a drawback into an advantage. That's very colorful, but also makes using aspects more work.
If you just go with the +2 bonus, this has the nice effect of making your efforts look more heroic. When you spend to get a +7, it's awesome, but bland. It's cooler to my mind if you also take into account that you had to do it while the floor is shaking (rolled a -2).
Either way, if you use an invocation for a reroll, this makes the story of the reroll much clearer, since it has now translated into a problem which has been overcome or worked around.
This also has some interesting interaction with bonuses, penalties and uncertainty. In this model, you can legitimately have someone roll fewer dice to simulate "lab conditions". In fact, if you think of that as pre-setting those dice to zero, then you could actually just fold penalties right into the dice.
Now, be aware this only really works if you take a light hand with bonuses and penalties, but doing so makes them much more concrete and makes them feel more toothy while actually making them a bit more normalizing. Consider - if you're rolling with a -2 penalty, you could generate anything from -6 to +2. If two of the dice a pre-flipped to -2, then the roll will be somewhere from -4 to 0. Now, some people might miss the more extreme outcomes, but I'd wager that the latter case will _feel_ more like the penalty mattered - both narratively as well as mechanically.
(as a bonus, you might allow aspect rerolls to "clear" a penalty, if you can come up with a justification for it, since a reroll represents a change of situation)