Quail already has a bunch of eggs
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Any chance you missed the eggs while cleaning or did you remove everything from the cage? 11 eggs in a 'couple of days' sounds rather unbelievable, is that really what you are saying? Or did you leave eggs in there while you were cleaning a couple of days ago?
11 is not really outrageous though, they can sit on that many. Some buttons never go broody, they just keep laying, so I don't really think she's insisting 'on having outrageous amounts of eggs', I just don't think she's becoming broody right away when she has a clutch.
I try to remove eggs from my buttons when there are 12 in a nest, if there is still no signs of a hen being broody. Then they can start over again with a fresh clutch.
The hen should go "broody" about once a month or so. She will lay one egg per day until she does go, so the best thing to do is let her keep the eggs and she will push the ones she wants into the nest and sit tightly when ready if there are any she kicks out or that are left around the cage you should remove them and toss them. Momma knows best. I remove the eggs every day from my hen as I don't want any chicks. She still gets broody but all I do for her is to be sure she can have as many cooling sand baths as she wants. The sand helps cool her breast like the eggs do, that is what broody is. Hot breasted! lol anyway good luck!
me.. these are the eggs I removed and she still has 2 with her.