What do you do on a song with only 4 chords you can find that go well? Make a riff based off the scale? Have a lead part? Change position of the chords? Change dynamics? Just change the singers melody?

Basically what do you do to your simple songs with not much else you can do?
Nothing (I'm not being snarky, that's true). With the way the audience is for songs like that nowadays, you don't need to do anything else. Write some catchy vocal hooks, maybe do some "do's," and write a bridge in the relative minor or major of the song. Instant hit, guaranteed.
Girl, I wanna do karate
Karate all over your body