Separate blogs for offices

I am trying to create a word press site that will have many offices. Each office will be a custom post type. Is there any way to make this work so every office can have their own blog that follows the navigation structure of

http://site.com/offices/office-name/blog

An single posts would be

http://site.com/offices/office-name/blog/postname

I realise that there is probably a multi-site solution , but is there a way to do this using CPTs ?