I have a 10, 9, and a 7 year old. The first two never fought until the 3rd came along. LOL! I guess 3 really is a crowd....but we all have to learn to get along.
First thing I learned in my parenting experience is that they all have different buttons. One will fight to get attention for me to be involved. The other will fight because she feels a need to be right, and the last one, he likes to do it just because he finds it entertaining to bug his sisters. So, I guess that makes them all wrong. Right?
I will also add that spanking, grounding from friends-media-etc, regular time-outs and long talks are not as nearly effective as any of the books who promote them make them out to be. In fact, I found one would work for one child, another for another child, and such, but no one of them works for all 3 of my kids.
Here is what has worked for us over the years.
1st...."if you hit, you sit and if you hurt people, you can't be with people." It doesn't matter who was at fault, who started the fight or who drove the other person crazy, the moment anyone "hurts" anyone else, that person becomes the ONLY one in trouble in our home, they are immediately separated from the rest until they can tell me what they should do in place of the physical behavior (note...not what they won't do, but what they WILL do). The consequenses are more serious now and usually involve hard labor as they are thinking. (as you will see later).
2nd. "Sorry has 3 parts"....you say it like you mean it (TO THE PERSON WRONGED! NOT THE PARENT TO GET OUT OF TROUBLE!), you fix it the best you can, and you make every effort to change your ways. (I wish our world would learn this, but so far I can only be responsible for these 3 future citizens).
3rd. The "chair talking time-out method"....when they were little -but old enough to talk things out, so they would learn to talk about feelings and issues, we would do a chair talking time-out. In that situation they each sit on a chair across from each other somewhere that I don't have to listen when they speak in a discussion tone of voice. They get to take turns talking about the problem and coming up with solutions. The rule is that they can't leave until they have a solution, they can't call names or say mean/insulting things and they can't hurt each other physically either. Whomever breaks that rule remains in a time out, and the other person gets to go do what they want. (even if it still isn't fair)
4th....works well now that they are older....and happened out of desparation last summer, when the young son (pesky for fun) and older sister (bossy for control) began to argue CONSTANTLY (mom-gone-crazy-time). "ANY ACTS OF DISRESPECT EARN CHORES". If they fight, drive me crazy, are rude to each other or anyone else, I give chores. I keep a list of my to-do's on hand, and they tend to get anything that is within their reaching level and doesn't involve cleaning chemicals assigned to them. They quit the fighting within two days, and my life became so much easier and my house so much cleaner.
So....no family is the same, and these may not work for you, but if it helps.....I figure the biggest thing in sibling rivalry is that it is their best opportunity to learn how to deal with conflict in respectful ways.
God bless and good luck!