True confessions: The game was written to intentionally spurn the d20. Haha. But I have since softened on that conceit.
I wrote a teens-piloting-mechas iteration called "Full Metal Jackals" that uses the d20 and adds results in the 13-20 ranged suited to missions/combat when in the mecha. In other iterations I have added a third category of "mission" or "combat" more generically. In those cases, 1-6 is the character, 7-12 the environment, and then 13-20 an optional list that comes into play when moving towards the scene's narrative goal (with some options for learning, progressing, etc.) or bringing in a predefined antagonist list (which makes writing monster stats a fun little exercise for "what can happen on a 13-20 with this or that monster?"). You just add the d20 to the list of MODIFIERS that tell you when to roll anything more than the traditional d8.
Love talking shop so feel free to share any ideas.