What a copyright does is protect the creator of the work against unlicensed / unauthorized use of what has been created. There can be multiple copyrights within a single presentation. For instance, in a book with illustrations, one copyright notice would identify the author of the text while another copyright statement would identify the artist of the illustrations. The artist obviously can’t claim copyright ownership of the text, just because of a contribution of art, nor can the writer claim ownership of the illustrations – it’s fine for both to co-exist within the same production.
So … speaking as a mere writer and author who’s been dealing with this for 25 years or so, not as a lawyer … I believe you can add your own copyright notice and still leave the designer’s in place. Something like: “All text copyright (circle c) ‘yourname’ 2007”.
What the designer mainly wants is credit (which is different from copyright), and especially for someone else not to claim credit.