When playing in the keys of G and D, try dropping the bottom E down to a D. There are some chords you may have to revise slightly but you get a real richness in the bass on the D/Dm chord. For a chord of G (well almost), the revision is 550030 (frets played from bottom to top). For chords of A and C, mute the bottom string, for an Em play 222000. When playing in the key of D, this tuning can be revised to drop the top E to a D too which then imparts a type of drone to the sound which can in the right circumstances sound quite good.

Other alternatives are quite drastic, like radical retuning to open or suspended tunings. You might still only use a basic three chords or so with little runs, but the sound can be quite extra extraordinary.