I can think of two ways. The first would be to use the simple "Approvals" option. This isn't truly a "process", so someone would need to add new approvers as the previous ones were approved to show true progression (also, you can an approvers to an Update on the Documents so they receive a description of what you are asking them to approve instead of just a generic "This needs approving" message).
The second way (which is probably more like what you are looking for with a true "process" or workflow) would be to create an Issue, which can have Approval Paths attached to them, and add the Document you want them to approve to the actual Issue instead of the higher levels Document tab. You might want to create a specific Issue type for Document Approvals so you can add your own Custom Fields and so forth.
