mixing a girl into a cage with two males could be a drastic mistake. The males could turn on each other, or turn on the female. I would usually not recommend trying it.
That being said, with separate cages they can live near each other. Tho you might need a way to make sure they can not see each other. You don't want to tempt the boys into fighting with each other.
I have my two boys in a FN cage next to my three girls in their own FN cage. (with several inches in between) But their is a large sheet of fleece in between to make sure they can not see each other. My father chin has a heart murmur and any time he lays eyes on 'his girl' and he cant get to her, he starts to have major medical problems. So he can never see her again. Chins have also been known to breed through the bars of separate cages. So you want to make sure you have enough room.
Also one time when one of my girls were in heat, my boys noticed right away. When they came out to play the could smell it even more and started to get a little aggressive with each other. I had to separate them for the next day.
Lots of things could go wrong mixing a girl with two boys. I do not recommend it.
