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There's plenty of crossover between the girls of all branches. Whether it's Reine and Fauna fishing, Anya and Sora playing raft, or Haachama and Mumei having a college girl war, they all talk frequently.
Meanwhile, even the girls who are infamous for collabing with Stars only do so occasionally. Ollie is probably the worst offender, but how often does she collab with them? A few times a year? Clearly there is a division between males and females, only crossing over on rare occasions.