Girl version of bleach ?
The beginning follows the same formula of 'seemingly normal boy has his life turned upside down due to a chance encounter with a girl who has mysterious powers', but there is more to it. Shana uses a sword in battle, but she is pretty much the only one using a sword. This isn't about sword fights per se. But no - the majority of characters are most certainly not 'normal'. Not nearly as action-oriented as Bleach.
I would suggest checking it out - chances are you would like it.
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