Need advice in setting up and then moving sub domain site

I am asked to design a website for a college. They want one main site and three sites on sub domains.

Their current website is hosted on a Windows server so I need to set up a new hosting account for WPMS. They don’t want their current domain name to change over until the new site is finished.

The problem I think I am facing is that I first have to develop and design the websites on a different (temporary) domain name. Then when all is finished I have to change the DNS settings of the old domain name to the new website. So, although the main WP installation doesn’t move to another location I would have to change all references from the temporary domain name to the one they are using now.

I would like some advice as to what is the best way to go with this. So any ideas are welcome. My question basically comes down to how to best develop a temporary WP MS and then have a new domain name for that website.

I hope everything is clear.

Thanks