I could eat a little more. (anything, I'm not full yet.)
This is correct.
I could eat it a little more. (some food)
Ok, but only in a very informal/casual sense. And even then it sounds a little unnatural. More natural to say: "I could eat (some) more of it".
I could have it a little more. (some food).
Like above. You can perhaps get away with very informally. Better to say, "I could have some more of it".