Some things that worked well for me when we added Gracie Ruth and then later, Yogi. I'd get on the floor and engage all of them in play. Boo doesn't like toys, but likes to wrestle. G didn't like to wrestle, but liked toys. So I would play with each one individually but at the same time. It seemed to help bond the pack a bit. Any time Boo would growl at G for getting in his way, I'd give him a quick touch on the neck and say no. Then go right back to playing with them both.
Give treats while sitting on the floor with all of them too. Carrots worked best because they saw me, pack leader, eating them and then sharing with them. I never gave out the treats in the same order, in other words, the same dog was never always first to receive the treats. I know a lot of people say to give the existing dog preferred treatment, but for my kids I found that showing them they were all on the same level to me worked best.
Walking is the very best way to bond the pack. If she hasn't had all her shots, you may want to get your vets ok before taking her out. But I would take them on short walks around the block. No stopping to sniff or get on the grass to try and limit contact were other dogs may have been. This above all else in my opinion, is what helped to them to bond and get along.
Good luck, give Max some time, don't allow Sophie to bully him - as puppies can do. But don't allow Max to be ugly either. You're the leader, lead.
