What is the best framework for PHP to build a custom document management solution?
It should be possible to build what you want very easily by customizing an existing application. Depending on what sort of access rights system you have in mind, you could build it with Drupal (finely granulated permissions), Joomla! (less finely granulated permissions), or even WordPress (simple level-based permission system)… But if you insist on building it from scratch, any MVC framework would do the trick. Take a look at CakePHP, CodeIgniter, and Symfony…