Maybe this could be handled with random questions.

Let's suppose that we want to select randomly one quiz from a bank of 3 quizzes (Quiz A, B and C) that each contains 4 questions ([A-1, A-2, A-3, A-4], [B-1, B-2, B-3, B-4] and [C-1, C-2, C-3, C-4]).

Question category 1 contains questions A-1, B-1 and C-1.

Question category 2 contains questions A-2, B-2 and C-2.

Question category 3 contains questions A-3, B-3 and C-3.

Question category 4 contains questions A-4, B-4 and C-4.

The teacher would set up a quiz with four random questions, each taken from the above four categories. Here's the modification: Moodle would select the same n^{th} random question in the four categories. For example, if n=1, the four random questions would be A-1, A-2, A-3 and A-4; if n=2, the four random questions would be B-1, B-2, B-3 and B-4; if n=3, the four random questions would be C-1, C-2, C-3 and C-4.

For my use, quizzes A, B, C, etc. would be slightly different versions of the same quiz. With a class of say forty students, I may not need that many different versions. Maybe five would already tell the students that they do not all have the same quiz, thus discouraging cheating. I could restrict the display of each quiz to different groups and that may do the trick, but having the option of random quiz built in Moodle would be nicer.