Will we get problems with too many male atiels and not enough females in a cage?

I and my fiance love keeping birds and currently have 2 lovebirds, 1 budgie, and 10 atiels. We have 6 males and 4 females. One female and one male have already paired. Will we get fights between the males if there isn't enough females? They are in a huge, spacious cage that is definitely big enough, it's pretty much an inside aviary cage, with lots of toys and feeders, and plenty of perches/flying space. They also have the cage door open during the day so they can come in and out as they please, although this part will be changing when I have my little girl in just over a month as I can't have birds all over her stuff..