Consider Burning Wheel's Fight! mechanics. You can play a fine BWr game without using Fight! at all, just using Bloody Versus. Fight! is a way to drill down on a situation and look at it much more closely than a single roll encourages. Similarly Hubris, Bring Down the Pain, etc. Each also has other effects, but there's definitely some common thread to be abstracted.
One possible problem is that if players are significantly more effective at one level than at the other, there is incentive to choose based on effectiveness rather than which looks like more fun. Playing a BWr character with very high Power and Speed but low weapon skill, for instance, you can win many Fight!s which you would lose were they Bloody Versus. In an ideal world you'd choose based on whether or not the table wanted to drill-down on the situation, and this choice wouldn't end up "screwing" a player skewed toward one or the other.
The main benefit, in my opinion, is that you can have several different sets of rules for different situations. Yes, I'm saying more rules is a benefit. :) Unified rulesets are elegant, messy situational rulesets have more descriptive power. So in BWr, you have Fight! drill-down for small-scale melee battles, Range and Cover for small-scale ranged battles, and Duel of Wits for small-scale social battles. Each has a very different feel and drills down on a different situation which could otherwise be resolved in one roll by the rest of the rules.
It's like playing a number of different games, connected through the story, shared resources, and some shared numbers. D&D, for example, feels like playing two different games: the game about adventurers taking on long odds and growing to become like gods interlaced with lots of games about miniatures battling it out on a grid. Or in Burning Empires, playing a game of planetary defense against the Vaylen while drilling down on specific aspects of the conflict which make up most of play.
I see two main uses of the drill-down that I care about. The first is in D&D, where (as far as I'm concerned) the goal is to connect a bunch of miniatures battles into a coherent whole. Here the drill-down is expected in every fighty conflict, and brings into question whether I should really even call it "drill-down" or not, because it's closer to abstracting up a level from the standard. The second is in BWr, where the goal is to have a fun minigame that explores a fighty conflict in more detail than the general rules can easily cover.
So when can I use this in extant games? What pitfalls are there in throwing a new drill-down into BWr, like a detailed spellcasting duel minigame, or in blanketing the entire thing in a metagame, like the Battle! rules attempt? These are on the face of it two very different questions, and at least for now I'll think about them separately.