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When you put it that way, I'd say that I wouldn't necessarily add the d20, but I would indeed add the 3rd list of "narrative goals" or other special things. This means that when you got the dice on your side, you go beyond just like "I do my thing" toward "we all move the narrative". Maybe this 3rd list could totally be collective, not individual.

I really like the potential here!

Oh, for sure. I think in default cases both the Character and Environment lists were meant to provide EFFECTS that are at the level of the whole group and the narrative. So adding a third category allows a designer to make the Environment truly about the setting/milieu/location and a Goal list then about the narrative l.

(If someone did want a d20, an adventure writer could fill up a 13-20 list as a pretty tight way to provide options for each scene or act in the story—almost like a Set Goal in Trophy, if you’re familiar).