Hello Ivica,
In fact, you don't have to set a closing date. You can allow multiple attempts, and if you unselect "Marks" everywhere ("During the attempt", "Immediately after the attempt" and "Later, while the quiz is still open"), students will only be able to see
their overall mark for the quiz in their gradebook even if multiple attempts are allowed . Note that when you allow multiple attempts, you must choose the grading method : "Highest grade", "Average grade", "First attempt" or "Last attempt". If you
select "Deferred feedback" for "How questions behave", under "Question behaviour", everything is automatically unselected for "During the attempt" under "Review options".