 If you liked
Mai-HiME
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 ...then you might like
Fate/stay night
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Battles of superpower and both have proxies of battle engaged characters. Like dolls.
Mai-Hime is similar to Fate/stay night because it is also a battle royal. Here normal schoolgirls are suddenly (or should I say born but not yet discovered) granted massive powers with as only purpose to destroy each other till one is left. The last one will then obtain a greater power to save the earth. Quite a dramatic story with lots of action.
If u liked Mai-Hime then i think u might like Fate Stay Night. Probably because both shows have a sort of master/servant relationships, for instance in f/sn Shirou and Saber and in Mai-Hime Mai and Kagutsuchi. Both shows have their moments of comedy and some badass moments so if u liked either of them i recommend u watch the other.
Just as in Fate/Stay Night we have several chosen fighters with powers that have to fight each other in order to achieve the final huge goal. These fights are constantly held after specific time.
Both series involve strong emotions and love.
One of the huge difference would be that in Mai HiME all fighters are females and that there is a different price to pay for a loser, which I would say in Mai HiME has more value.
A human gains control of a strong entity in which they are forced to battle others that are in the same situation. The battles are either to the death, or until the strong entity can no longer fight. The fights stop when there is one victor. The battle is supposed to be kept quiet and only amongst the participants, but the fights escalate and soon, the entire city is at stake. Outside of the fighting, they live normal lives.