The main thing, of course, was homeschooling. We didn't start until their 6th grade, 3rd grade and 1st grade years, but homeschooling was the best thing we did for our kids. They spent a lot of time together, which helps with siblings being friends. We also did a couple of things to help them learn to negotiate, one was a "kid of the day" system. Each kid had 2 days a week where they were the kid of the day. I took the extra one. On that day, if there was a dispute that couldn't be solved or a choice to be made, the kid of the day won it. If we were out and about and needed to get something to eat, the kid of the day chose the restaurant. The kid of the day got to choose the TV shows at Grandma's house where they had cable, which led to the hilarious mix-up one day when they thought it was youngest son's day, but it was oldest son's day. Oldest looked at youngest and said dramatically "You made me watch Spongebob!"
Another thing that may have contributed to our success with adult kids who get along and really love each other, is the screen time limits. Since screens could not come on until 6 to 7 pm (It changed over the years) they kind of had to interact throughout the day. They had school together and then they had free time without screens together. They played a lot. They had elaborate play scenarios that would range all over the house and outside. They constructed huge things in the living room out of books, video cassettes, Lego, K-nex, etc. and of course, pillow and blanket forts.
The main thing I did though, was to coach them on how to compromise. If they had a toy they were fighting over, at first I would talk them through a compromise where one could play with it for a predetermined period of time, then the other one would get it. Kid of the day would get to go first. We'd come up with ideas where each could be overall happy with the plan. Then as they got better at this, I started trying to get them to compromise without involving me at all. I did this by solving the problem most efficiently, if they were fighting over the toy, I'd take the toy away for the day. If they were fighting over TV shows, I'd turn the TV off the rest of the day. I'd say "you have 2 minutes to work something out or the TV goes off for the day" (or "the toy is mine!") and let me tell you, they learned how to work things out.
I emphasized that we were a team. When my oldest broke his ankle and we had to take him to immediate care, one of the other kids started whining about something and I said, "we're a team" and the whining stopped. Everyone knew that the oldest had to come first at that time. When he had to be non-weight-bearing on that ankle for 14 weeks (not even resting it on the ground when he was sitting) the other 2 kids waited on him hand and foot, without complaining.
Of course, they occasionally get on each other's nerves. Sometimes somebody needs to retreat a bit, go outside, go in their rooms and set boundaries on how much one person can talk to another person without a break. ;-) (Some of us are very, very talkative and other people need to THINK!) Our family is not perfect, but the kids get along very well. People have commented on it many times when we have spent a lot of time with them, so I know it's unusual, but it's not difficult to do.
I credit Parent's Magazine for the kid of the day idea.