It depends on whether you're talking about a countable quantity. There ARE even more eggs, but there IS even more milk.
'ne' = 'of them', which isn't in the Italian sentence (though probably commonly would be found there, just like in English)
It is not correct in Italian. You say: "Ce ne sono di più". (The correct translation of this phrase is "Forse ce ne sono addirittura di più")
"Ci sono di più" is absolutely wrong!
At first I didn't understand the meaning of this phrase because of this mistake (and I'm Italian).