There is an interesting article, “Create your own private Twitter site using WordPress” at Cats Who Code on how to build a MicroBlogging type of site using WordPress to create a Twitter like network for family, friends or company.
It uses a special free WordPress theme for social microblogging, called P2
Info at : http://www.catswhocode.com/blog/create-your-own-private-twitter-site-using-wordpress