There's 'Sailor Moon'. The Sailor Scouts often have their little spats and disagreements which can be seen as a form of 'catfighting' in a sense. But they also work together against common enemies. The story is about friendship, love, and saving the world, and these catfighting - like moments add some interesting drama to the overall plot.
In 'Revolutionary Girl Utena', there are complex relationships and power struggles among the female characters. There are scenes where they seem to be in conflict with each other, which could be considered in the realm of 'catfighting' in a more metaphorical way. It's a very deep and thought - provoking anime that explores themes like identity and gender roles.