I won't swear to it, but even if you can actually locate an upgrade version of Web Premium CS3, I don't think it will install using Design Premium as a qualifying product. That said, as long as you don't uninstall the previous versions of most Adobe apps, including everything in the Web or Design packages except Acrobat, installing a newer version will not interfere with the older versions.
I believe it will but you must find the right upgrade and finding a CS5.5 upgrade is not going to be easy. Why not just get the CS6 Web and Design Premium package (that eligibility ends soon) or better yet, take advantage of the intro pricing for Creative Cloud. At $29.99/month it’s a bargain: http://www.adobe.com/products/creativecloud.html