I want to start a new wordpress.com or blogger.com

Is it possible to use wordpress with some plugins or implement som changes so that I can set up a bloggserver where anyone can sign up for a free account and to start blog on my server?

Everyone of the bloggsoftwares I have found so far assumes I want a bloggserver just for my own – I want to host a bloggcommunity where anyone can sign upp for a free account.