Since you already have the chords and rhythm coming through in the acoustic guitar part you have quite a few options you could explore.
Instead of playing low chords and letting them sustain, try playing higher chords and either letting them sustain or picking through them. You can pick through them in a similar rhythm with the acoustic or experiment with alternate rhythms. Also, explore higher chords played only on three or four strings instead of all six. I've found some really cool sounds like that.
Doubling the melody, creating a harmony part to play with the melody, or just coming up with simple melodic lines that compliment the melody of the song you're playing are all good options. You can do this all the way through the song or intermittently between chords. When using chords in this style of playing it helps to find chord formations or inversions that run smoothly between the melodic lines you've created.
Playing through arpeggios slowly and utilizing unique sounds like harmonics are also good options for interesting, but not flashy, back up guitar parts. I know talking about guitar without any tabs or recordings is kind of abstract. Let me know if this needs any sort of clarification.