Auto-assignment by roles

Is it possible to make auto-assignment of a document not only to an individual employee, but auto-assignment by roles, so that the document is simultaneously assigned to all employees who have this role enabled?

No, currently the assignment rule works on user-level wise. You have to select and add users in the assignment rule for the auto assignment to work. Could you elaborate this requirement with a use case for better understanding?

I need to automatically assign several employees from the same department to one document, since it is not known in advance which of them will be able to complete the task at the moment.
To be able to start execution, the one who is the first will be free.