I friend who ran a long and complete 5e campaign plans to run his next campaign in Planescape. He as more of a story gaming bent, but asked me advice on how to make Planescape feel different and how to include the types of "success, but" or "failure, but" mechanics he likes from games like Star Wars: Edge of the Empire. My suggestion:
Planar Intervention
Whenever you roll a natural 1 or natural 20, in addition to your success and failure one of the 9 alignment planes has influenced the situation positively or negatively. Roll d20 to see which (odd numbers are positive, even are negative), a natural 1 or 20 means it's the plane matching your character's alignment. Each plane should have a list of effects the DM picks from or rolls from to see. Example:
Chaotic Good - Arborea
1. Plants grow in an unexpected place, hindering or aiding progress (thorns blocking a path, vines providing a ladder)
2. A surge of emotions grips you or someone nearby, joy, wrath, fear, etc.
You get the idea. The tables would be different enough that your alignment would matter, and certain places would ofc. resist/bring forth certain planes more than others.