Right. I am afraid to say that this would be an extremely difficult modifcation to make in the existing quiz module. There is a fairly fundamental assumption throughout the code that each question is independent.
This is a relevant forum thread: https://moodle.org/mod/forum/discuss.php?d=328970#p1323499. If what was talked about vaguly there ever got implemented, then the kind of thing you want to do might become possible. However, that is all hypothetical for now.
Until then, as Daniel says, you would need to make a new separate activity.