Can I have /blog and /foo and /bar all point to the same blog?

It’s generally consider pretty bad practice to have the same content at different URLs on a site and will probably damage your search engine performance. Bear in mind you’ll likely need to use a rel="canonical" link tag in your page header pointing to one of the three possible URLs.

Also WordPress stores many links directly in its database and these also will point to one of the possible locations in particular, meaning you’ll never be able to preserve links on /foo/* to /foo/* if the /bar/* version of the link has been stored in the wp_posts content table in the DB.

So the further question I’m left with is why do you want to do this? What particular problem are you wanting to solve?