One idea is to tell them they have lost the "privilege" of playing with each other and make them each chose a room to be in doing their own activity; I've found that this works pretty well because they generally all want to be in the same room (living room) near me (kitchen) and so that helps break up the fighting energy and then they try again to make it (whatever the conflict is) work. I also try to pump up the "sibling unity" by making up little songs about them, talking about my own sister with love, and talking about our family as "The Walker Family." This helps!

Sibling rivalries can be really hard to handle. I've had a hard time with my son and daughter fighting constantly. It may not be what you want to hear, but honestly it just takes time. Once my kids started to mature, the fighting and rivalry died down. Until then, keep tabs on the rivalry to make sure that it doesn't become permanent. When it seems like one of the kids has taken it too far, make it clear that what they did wasn't okay. Have them apologize to their sibling, and put your foot down when it comes to competitive behavior for the next few days. Encourage your kids to focus on competing with themselves instead of each other. 

I personally have a twin brother so I know all about sibling rivalries! What I never thought would happen when I was little is my reality now-- my brother and I are best friends! This happened after college and now our kids are friends too.

How old are your children? My eldest daughter and son are two years apart and they often fight because they are so close in age. In comparison, my daughter and youngest son are further apart in age and they have more of a mentor relationship because my youngest looks up to her and she looks after him.