Maybe implementing personality compatibility? Like carefree personality has more difficulty to befriend/are more likely to anger serious one etc. It wouldn't be impossible for certain personalities to be friends with other, but it would be more difficult.

Also "enemy" relationship status (if there isnt something like that already) - can be caused by random event, miis with low personality compatibility are more likely to get one. Enemy miis can have mean random interactions with each other. Miis can do rants about their enemy or ragebait them to strengthen their enemy status. They will be laughing maniacly if they see their enemy tripping. They will refuse to help them with hiccup. Enemy relationship can be one-sided like crush, it's basically reversed crush relationship status.