Subdirectory Setup

I have multisite setup up and everything is working except I can’t figure out how to add a new site within another subdirectory.

I can make a new site at: http://www.mysite.com/new-site

I want to be able to add a new site to: http://www.mysite.com/network/new-site

I would really like to be able to add a new site to: http://www.mysite.com/network/state/new-site

How do I do this? Do I need to change something in my wp-config or .htaccess files?

Thanks in advance.