Ugh... this JUST happened to us. We started with two hens and lost one when the temperature dropped a near 40 degrees and then shot back up. Because of the impending winter, we wanted to ensure we had other chickens to keep our surviving hen warm and social. The integration was fine, it was like the Thunder-dome for a day and then things settled. But as it turned out the two new chickens brought a terrible pecking behaviour with them.
Many butt feathers were lost over the holidays and things were getting really bloody which was not helping. I did a ton of research and tried just about everything, but our chickens are living pretty good lives so I was running out of possible changes to make. Two weeks ago I spent the day sewing saddles for all three of them. Even though they are not all getting pecked, they all needed to have jackets to avoid bullying. They hated it at first, but after a day or two things settled down. So far, I'm comfortable saying it has worked. They look ridiculous, but there hasn't been anymore pecking and feathers are growing back.