 If you liked
Kanojo to Kanojo no Neko
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 ...then you might like
Dareka no Manazashi
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They are touching short stories made by Makoto Shinkai. Both stories include a girl & a cat with a similar premise of going through the hardships of the working life in the cat's point of view.
Both are animated short-films revolving around rather, narrating the lives of two girls, individually. The stories in both the works of Makoto Shinkai are narrated throughout by an unknown narrator whose identity gets revealed in the climax, in a subtle yet beautiful manner.
Both the stories involve cats who form the essential element of the short-films.
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Recommended by WolfCladInBlack
Special ones, including pets. She and Her Cat and Someone's Gaze are both anime following narrated family lives, with people who create bonds as far as between humans and pets. Both anime having pets being with a cat.
Both are good short anime, made by the same director Makoto Shinkai.
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Recommended by NextUniverse