I don't intervene on arguments.
Have a Respect Day and declare that nobody is allowed to say anything negative. Have a game where everyone has to say good things about the person sitting to their left and go round in a circle doing that. Teach them, say it over and over until it's their philosophy too, "If you can't say something nice don't say anything at all." Make them learn to use their words to build each other up rather than tear down.
When my ds and dd fight badly, I tell my ds a long tale involving him being a grown up man with no friends, and he has a sister, and he phones her but she just puts the answering machine on because she hates her brother. I say, this could be your adult life, how does that sound? My son gets freaked out by the idea of being a friendless adult whose sister won't talk to him.
I guess I'm quite lucky with my children because their personalities mean they are close, much as I was with my sister. But children will do whatever they can get away with. If you've let them get away with living in a house where they are free to ridicule and put each other down and destroy each other's happiness then you reap what you sow. You have to nip that kind of behaviour in the bud.
Another thing I do is - don't take sides, don't intervene, you're not teaching them anything useful if they're helpless without you acting like the United Nations in their midst. I'm incredibly harsh and arbitrary and the children have to learn to work together to work around me. For instance - they get a toy, a gadget to play with. I say "Agree amongst yourselves how long each one has it." And then they do and they leave me alone (This is the main goal all along - LEAVE ME ALONE!) If one comes in whining "He/she had it longer! Not fair it's my turn!" I say to them, "You can't work this out between yourselves, give the gadget to mummy." They learn then either sort it out themselves or I will take it away. And I do, I just take stuff away, too bad if they whine about it.
Another thing I do is force them not to say "ME I WANT IT." I make them have long debates where they prefer each other. "No, it is your turn," "No really, it's your turn." And in doing this I hope they learn what I'm after which is for them to stop being selfish. Even if they are only playacting.
Expect them on a regular basis to be excellent towards each other, or there will be punishment. Good luck.