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The way they're planning it now is really, really a bad idea. First you put a part of the new design. New url's start popping up. SE's crawl that, might find duplicate content, you need redirects in place, but what happens when the site is moved again, you have to change redirects again... So it sucks! You can put everything on the www2 domain, but put a noindex nofollow in the header. Better still would just to let the new website sit behind an authentication screen so only you, developers, etc. can reach it. Once it's fully ready and you know what all the new urls will be, setup redirects (301's!) and once they are ready to go, than move the new site in place.