Firewalling the Fiction [The Hellenes/Mask of the Emperor]

I've noticed that in most games I've played, you consult with Fortune once (one roll of the dice, one card drawn, etc.) and then return to narration. For example, I roll to kill my opponent, he rolls in response, and then back to narration with the dice results in mind.

I'm wondering - are there any games anyone can think of that have a series of rolls, etc., occur before going back to the fiction? A flurry of dice-rolling, and then narration, for example, as my foe and I charge up and down the floor in our duel, possibly with each subsequent dice roll building off the results of the first, and at the end, we get a great big mass of information to use while we narrate. Anyone know of a game like that?

The reason I ask is that I've taken a shine to Vincent's clouds-and-dice analogy, and it rings true for the current version of Mask of the Emperor - it's possible to roll quite a bit of dice without ever taking any information from the "cloud"/the fiction, only taking info from the dice, and that does feel kind of "firewalled" or limiting, like dice-mode and talkie-mode are two very distinct, discrete play modes; this is not a pleasant thing to experience. I think I've found a way to correct the problem, but now I'm wondering if there needs to be sort of a 1:1 ratio of dice-narrative-dice during a Point of Contact with the mechanics, or if that's just how it's usually done.

Thanks, all!