You could certainly set up this type of quiz but it would require a little bit of work.
The easiest way would be if your course is using New Quizzes, which allows you to duplicate a quiz (follow the instructions in this lesson but locate the quiz you want to copy: How do I duplicate an assignment?) You'd have to edit the name of each copied quiz and the due date, but that way you wouldn't have to redo all the questions in the quiz itself.
If your course is using Classic Quizzes, duplicating a quiz isn't supported. I'd recommend turning on New Quizzes and migrating the quiz you want to copy so it's in the New Quizzes format. (You can still create additional quizzes for your course in the Classic Quizzes format if you prefer.)
If New Quizzes isn't an option, you can create the questions in a question bank, create a quiz using the classic format, and import the question bank. And then do that a bunch of times.