Also be sure to never make a deal out of it when they meet no matter what happens because that can make the aggression worse.
If they have a little spat, just try and stay calm and don't say anything but if they are fighting just gently pull them away from each other if they are causing injury....which I think would be very unlikely. This is most like to happen after human intervention has already ruined the dogs chances of resolving things on their own.
The odd spat here and there between any dogs that live together is nothing to worry about and they often just flash the teeth, one might pin the other down and do a lot of growling and snarling but no biting takes place and no injury and if they do bite, the bites are superficial with no real pressure applied. It looks quite severe to us but its just a little ticking off in a dogs books. They are pretty good at sorting things themselves though so you should be ok.
I'm sure your new addition will gradually get used to the other two dogs but try and keep it one at a time at first as mentioned so she isn't overwelmed.
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