If I understand your post, it doesn’t sound to me like the three or four quizzes need to be separated in the workflow. Say the workflow looks like this
In Stage 3, you could put the quizzes in the same form with each quiz on different pages. Of course, the quizzes could span multiple pages, depending on size, so you could have some kind of navigation scheme so they could move between the quizzes.
When a quiz is completed, give the user some kind of indication (maybe as part of the navigation scheme), and you can choose to hide or disable each quiz when it’s complete if necessary. Once all the quizzes are complete, then you can move to the next stage.
Hope that makes sense.