]As has been pointed out a couple of times, you can have as many quizzes started as you like if you work on them in Word. I compose all of my quizzes in Word because I am a very poor typist. Word catches a lot of my errors.
I used to use MS Word, and sometimes will do now and again, but lately I've been very happy with a fantastic FREE general purpose text editor for MacOS called TextWrangler. It has some very powerful capabilities, like 'grep' searching and also spell-checking, without being cycle-chomping bloatware.

After all, we can only do unstyled text anyways in our quizzes, so a lot of the advantages of word processors (designed for generating documents of styled text suitable for printing) are not applicable.
I've been writing a lot of grid logic puzzles lately, so the grep sort/extraction capabilities are really handy for the way I write them (which in some respects isn't very logical at all).
I'm sure there's an equivalent for Windows.
The newest Word may do grep now, but there is all this overhead in word processor that's not in a text editor, you see. And did I mention it's free?
It's just something I offer as an alternative for quiz writing. It's good to have options.