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".

The first sentence makes perfect sense and is understandable. The other 2 are understandable but the phrasing sounds slightly odd. It would be more natural to say “I could eat a little more of it” and “I could have a little more of it”