I need a document management system that will integrate with a subscription system. There will be multiple subscriptions with different levels of access required.

Is there a subscription extension that is compatible with Joomdoc?

Hello, JoomDOC3 hasn't subscription system. What type of subscription do you want? We can make it as paid customization.

I was looking for something like Akeeba Subscriptions which integrates with Docman.

The site is a subscription site with various different subscription levels and users can access and download documents that are accessible to that subscription. Akeeba Subscriptions manages expirations and automatically removes members from the relevent Docman groups when their subscription expires but leaves them in allowed groups (ie free access).

Sorry, JoomDOC3 hasn't such functionality.