I'm new to keeping the species but everything I read on their husbandry and natural behavior says that button quail are monogamous and you cannot keep four of different sexes together once they grow up without some very bad fighting, so I'd recommend pairing them off once they are older (they look young, or are they all girls? If the latter you may be okay..)
That cage will be hard to clean with finches and quails in it. Mine are pretty calm, I can just scoop bedding out and they run to the other side and kinda pace but don't freak out. You'll have to try and scoop out through that door, maybe clip a towel over it so they dont fly through? The quails will freak out but you'll have to work around them unless you can herd them into a box to take them out each cleaning. But that will stress them.
I have a lot of finches too but I keep them in a larger cage with a pull-out tray. For yours I'd recommend some more perches, some silk greenery to hide in and a swing or two. Only keep a nest in if you want them to breed, otherwise it encourages zebra finch hens to lay eggs constantly and males to get aggressive.
I have 7 society finch in here... 30 x 18 x 36 high. They do have a nest as this species is much more good natured and I switch their eggs with fakes for population control or is have dozens.
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