Is there a way to allow an additional attempt on an Assignment like with Quizzes?

If an instructor limits the number of attempts allowed for an assignment, is there a way to moderate and allow a specific student an additional attempt like this option for quizzes?   NOTE: I ...

Self-enroll as a role other than student

Is it possible to allow authenticated user to self enroll in specific courses as a custom role rather than as a student? Thank you, C