I had one male and five females all together, and when the male chose a first mate it was that female, not my male, who started harassing the other birds! I had to separate them from the others. Luckily i had another cage handy so i was able to prevent any injuries. The remaining females all live together quite happily and even preen one another.
There's evidence to suggest that quail are sufficiently domesticated to be kept in groups, especially if you have lots of room, hides, and multiple areas for food and water. Their natural state is to live in pairs, though, and they may revert to their natural territorial behaviors -which can include killing or mutilating offending birds- with no prior warning.
I hypothesize that territorial behavior will be passed down from territorial parents to chicks. I don't have any real scientific evidence to support this, though, and most breeders are more concerned about breeding for size and color than temperament. I guess it remains to be seen!
It's probably best to be prepared to separate your pairs if necessary. Better to have a plan B and not need to implement it than not have one and need it!