I had a different problem, i introduced my Buttons and Cots together and my Buttons got beat up. Then, i changed them to different pens and then i introduced em together after some time and my Buttons beat up my Cots. (Cots beating up Buttons means Cots chase Buttons and peck at them) (Buttons beating up Cots means they jump in the air and peck at their eyes)Well, I'm pretty sure you couldn't keep CPQ's with chickens (they'd probably eat them) but before the great quail massacre (**** mink) I kept eight cots with three cream crested legbars and they got along well. The quail had their own sleeping quarters, but they lived in the same run. sometimes the chooks even gave the quail mealworms from my hand.
(Buttons are territorial, Cots... not so much)