I don't want any more. I just want more of more.

Elisabeth is very fond of those things that are spread on bread: cream cheese, butter, jelly, peanut butter. In fact, she is so fond of the spreads that she often eats them, and leaves the bread (i.e. she licks the spread off the bread).

Just now she finished extracting the peanut butter from a piece of bread and declared:

I don't want any more. I just want more of more.

I trust you understand now what she meant.