Notes on Modes
Dm - D Dorian (C Major), D Phrygian (Bb Major), D Aeolian (F Major) Am - A Dorian (G Major), A Phrygian (F Major), A Aeolian (C Major) When you have a minor chord, you can technically get away with playing any of the minor modes; Dorian, Phrygian, Aeolian, and maybe Locrian; as guitarchitect pointed out. Same goes for major chords and the major modes. I like to call it a loop hole, rather than doing mental gymnastics , in figuring out all the keys that will accommodate a specific chord on the fly.