Multisite Question

Hi, before I go through the trouble of setting of MU I would like to know if what I want is possible. I have a website where I would like the blog to be a different domain, but share the theme. I would like it to be where the main site and every page but the blog is (for example) frog.com, but when you click on blog, it is cat.com. And this blog at cat.com is simply using the blog “Page” of the frog.com’s theme.

Does that make sense?