I think that we're getting into the logic thing here, Ptak. Of course you may eat more - if I let you have more. As GWB said, it would be unusual to hear "eat" used in this way.Thanks, GreenWhiteBlue.
But is it just a politeness (what we would say being someone's guest) or does "eat" sounds really bad there? I mean, if people who are quite close are speaking? Say, a husband and a wife. In this case 'eat' is also bad?
In the same way, a wife might say to her husband at the dinner table "Please give me some more roast beef", but it would seem very odd to hear her say "please feed me some more roast beef".
One can also say "can I buy more" if one is shopping in a supermarket, or "can I sell more", if one is working in a store, but none of these has much to do with the original situation about which the question was asked, has it?How about asking my nutrition consultant "Can I eat a little more? or Can I eat a bit more" if I am on diet?