Broody Italian quail
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Any change is likely to cause her to abandon the eggs - but other quail being around her is likely to as well, unless they have very much room. If she is far away from the cage door, I guess you might be able to sneak at least some of the others out, but I wouldn't even try it unless it's possible to place them in a cage right next to the one she is in, where they can see each other. With a chicken, you can usually move it and it stays broody, I would not try this with a quail.
Well.. For now, it's probably more of a big 'IF'. But, should you get near hatching date and she is still on the eggs, I'd keep a very close eye on her. If they are on wire or the cage is otherwise unsuited for chicks, I'd remove her after the chicks hatch. If the cage is okay for chicks, I'd remove the other quail as soon as I see a chick or empty egg shell. I might do this even if I decided on removing the mother and chicks actually, to make sure the chicks that hatch first aren't hurt by the other quail while the rest of the chicks hatch. I think the sound of the hatched chicks will keep her broody no matter what changes you do, but she might still abandon a nest of pipped eggs if one or more chicks hatch before the rest.
It's quite exciting ^^ I don't have coturnix myself, but I have button quail and my 3 hens hatched about 25 chicks between them last year.
I kept 3 of the female chicks, so this year I have 6 hens. 4 have been broody, but 3 of those seem to have abandoned their eggs within a week of becoming broody, so only one left. I think she is about at day 10 now, so I have my fingers crossed :)
With the buttons I'm not that worried about the other quail, in my experience they actually tend to end up helping to take care of the chicks. But they live in cages that are so large I can easily place a smaller cage on top of any trouble makers for a few days, to allow the chicks to get a little stronger before releasing the trouble maker again. However, I've heard that both buttons and coturnix - in some instances, even the mother of the chicks - are prone to aggression towards chicks.
It's great if she is accepting to be cornered off. Do you have any pictures of your set-up?