If you liked
Sakamichi no Apollon
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...then you might like
Given
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Kids on the Slope and Given connect based on music mostly, but there’s also the theme of friendship and romance present in both. In both of them, two people get closer based on their love for music, and the main protagonists are both new to what they’re doing.
If you liked
Serial Experiments Lain
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...then you might like
Perfect Blue
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Lain and Perfect Blue have a lot in common, starting with the theme of reality. Both make the audience question what is actually real, and both have storylines that might require rewatching to figure out. They are both highly psychological, and they are calm, but anxiety inducing, for the most part.
If you liked
Sword Art Online
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...then you might like
Dungeon ni Deai wo Motomeru no wa Machigatteiru Darou ka
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Both Sword Art Online and Danmachi have very similar settings, being inside a game, and have similar plots. Both are about a male protagonist that’s in a game and has to level up in order to reach his goal, along with a female partner there beside him. Speaking on the settings, both are extremely similar, even containing towers that have enemies on every level that are required to be defeated before moving on.
If you liked
Mirai Nikki (TV)
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...then you might like
Happy Sugar Life
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Mirai Nikki and Happy Sugar Life both have yandere as their main character. They are extremely protective over the other main character, and the wish of the yandere is that they can end up happy and together with the other main character, without any “obstacles” in their way.
If you liked
Deadman Wonderland
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...then you might like
Tokyo Ghoul
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Tokyo Ghoul and Deadman Wonderland are both about normal students who gain abilities. After gaining those abilities, they have to fight against organizations that the civilians trust, making it harder for them to accomplish goals. Both contain gore, fights, and a lot of obstacles being randomly thrown in (to the main characters’ surprise).
If you liked
Tokyo Ghoul
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...then you might like
Bungou Stray Dogs
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Both have a similar plotline, and both revolve around a group that is fighting against an organization. Both also explore the ability to use powers, and when they are able to control those abilities.