I am not a lawyer, but an editor--which gives me some experience to draw on to comment on this. And that experience tells me that as long as you craft your contract clearly, the illustrator will only have copyright in their illustrations. They will not acquire any rights to your character from having illustrated the character in one book, and you would be able to change illustrators. So you do not need to pay more to buy the copyright from the illustrator.
Of course, if the original illustrator holds copyright in the illustrations, a new one could not copy one of the illustrations in a new book, but that's a different issue.