How to create custom URLs for Custom Post Type sub sections?

Not sure how to ask this, because I’m not exactly sure what I’m asking.

I’m looking to use custom URLs (using rewrite rules maybe?) to create ‘tabs’ for a Custom Post Type. In the past I’ve used things like a GET session variable to determine what tab the user is on, or JavaScript. I would really prefer to keep it on it’s own logical page with a URL to reflect that.

A very basic look of the tabs would be:

HOME | UPDATES | CONTRIBUTORS | WALL

For example if we’re on the CPT of Charity’s sub page of Updates: http://siteroot/charity/updates