So it has to be three assignments. But if you just want a digital drop box, that is, a place where student can just upload files you can implement it in the database activity. You can set up the entry form to contain a file field. Students will able to upload as many files as you want by adding entries. If you set the database to require approval and never approve students can see only there own entries.

The teacher can turn off "send for marking" which allows students to constantly upload and delete files. Also a teacher can allow a student to resend files that have been submitted for marking.When the teacher goes to grade the assignment, she can then click "Revert to draft" which allows the student to edit the files again. However it seems like having three separate assignments is that way to go if there are three separate due dates.