The easiest way to mix in new birds with minimal fighting is to separate the new birds on the other side of a fence, so that everybody sees everybody and aggressions are worked out from behind a fence. No touching, only looking. Let the new birds stay on the other side for 3 weeks or so. When the day comes to release the new birds in, they will have gotten to know each other somewhat and the fighting should be less if any. There will still be jostling for position, but it is less likely to get blood shed.
However, stand guard for any brutality. Stick around the chicken yard for at least an hour and check them throughout the day and following days. If anybody starts to get too violent, separate out the aggressors, not the new ones. This will let the newbies work their way into the pecking order.
Keep the aggressor away for a week and then re introduce the aggressor. By then the new birds have adjusted and the aggressor will have lost some edge. Hopefully. LOL
Good luck with your new birds!