If you liked
Ano Hi Mita Hana no Namae wo Bokutachi wa Mada Shiranai.
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...then you might like
Kimi no Na wa.
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Similar premise. Similar art style and story telling.
If you liked
Rec
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...then you might like
White Album 2
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The two series are similar to the skeleton. But have different body parts. The two share a sort of fated meeting of a future lovers couple. Whereas one deals with music, the other deals with voice acting.
If you liked
Boku dake ga Inai Machi
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...then you might like
Re:Zero kara Hajimeru Isekai Seikatsu
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Both anime have a few things in common. Dealing with time travel and a heroine going back in time to help someone special. The both have received good reviews and plenty of reason to watch.
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If you liked
White Album 2
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...then you might like
Shigatsu wa Kimi no Uso
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I'd recommend watching this after Your Lie in April, for two reasons. Firstly with WA2 compared to YLIA are similar but totally different. White Album 2 handles a similar theme, but for a more mature audience. It's the older teenage version in my opinion. Secondly, the two anime are so similar in a lot of aspects. Musically charged themes, to forward character development and relationships. I'd highly recommend watching both a seeing for yourself.