If you liked
Aoki Hagane no Arpeggio: Ars Nova
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...then you might like
Kantai Collection: KanColle
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These two anime have a different plot but they use the names of Japanese WW2 ships. The "Abyssals" and the "Fleet of the Mist" are enemies that seemingly appear out of thin air and force the ships to attack them. Kancolle has a faceless admiral while Ars Nova has a captain that commands from inside his submarine Iona (1-401). Kancolle will be receiving a second season and will hopefully introduce submarines and ships in the game that were not seen in the first season. If you enjoyed the action and navel tactics in Kancolle you should watch Ars Nova. Keep in mind Ars Nova is much more futuristic and Kancolle follows historic battles that occurred in WW2.
If you liked
Rakudai Kishi no Cavalry
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...then you might like
Gakusen Toshi Asterisk
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From what has come out thus far these two anime are extremely similar. They include a protagonist who seem weak but when they have their skills tested, they turn out to be very strong. The female leads in both anime are from a noble family and use fire in their attacks. Both anime incorporate a contest/tournament to determine the strongest warrior.
If you liked
K-On!
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...then you might like
Tamako Market
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To start off Tamako Market and K-On are from the same animation studio (Kyoto Animations) Both anime are light and fluffy. Tamako and Yui are very similar in their unwavering smile and that almost nothing can dampen their spirit. Both anime are slice of life and revolve around a close group of friends where eventually more characters are added. I truly loved both anime and i hope you will as well.
If you liked
Akame ga Kill!
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...then you might like
Tokyo Ghoul
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These two have a similar story. The MC both start as weak and alone but they eventually gain strength and they learn the importance of friendship. They also both go against the societies they live in. Tatsumi and Kaneki both fully experience the cruel reality of the world they live in. Akame ga Kill and Tokyo Ghoul were both based off their respective manga's. If you have seen one you should watch the other, if you haven't seen either you should watch both.
If you liked
Stella Jogakuin Koutou-ka C³-bu
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...then you might like
Sabage-bu!
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Both shows include a group of girls playing around with airsoft guns. Sabagebu has a more lighthearted tone. Stella Jogakuin Koutou-ka C³-bu is lighthearted at first but quickly becomes -competitive. It goes into the bonds between the girls and how they sort out their past disputes.
If you liked
The iDOLM@STER
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...then you might like
Love Live! School Idol Project
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-Both anime include idol groups -Interesting and lovable characters -In Love Live the girls form the group to save their school whilst in Idolmaster it goes into the routine of idols trying to get into the pro scene. If you have seen one you would love the other and if you haven't seen either it wouldn't hurt to watch both.