NILIF is great, but I'm not sure that it would solve the fighting issue. You can try it though.

Easy-going dogs can be treated equally, but sometimes you do need to give one preferential treatment. I know it sounds horrible at first, but if you think about it and research it, it will make more sense. Dogs live in a hierarchy and are used to "pack mentality". Studying wolves will give you a lot of insight on this. The "top dog" establishes his rank and the humans need to respect that. Most of the time, the other dogs are fine with taking subordinate roles. You run into issues when you have more than one dog fighting for the same rank or when there is confusion as to the pecking order. If the humans make it clear what the rankings are, the dogs' relationships will fall into line. You should always observe them to see who THEY decide the alpha is, and then treat that dog as alpha. Treating a lower ranking dog as alpha will sometimes create some chaos in relationships among the dogs.

They should all look up to the humans as higher than themselves, which is where NILIF comes in handy. But they also sometimes need rankings within themselves too.