Allowing Modules to be Shared with Select Authors Only

Is it possible when adding modules to make these shared with a select author(s) only?

What I am trying to do, is to allow learners to upload assignments to the course page, which is not possible from what I understood. Kindly confirm.

So to get around that, I am experimenting the option of giving them author rights to upload modules with their assignments. However, when they select 'shared', it makes their assignments available to everyone. Hence, is there a way for them to limit the sharing to their trainer only?

Thank you.