 If you liked
Serial Experiments Lain
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 ...then you might like
Kaguya-hime no Monogatari
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While the settings may be totally different for both series, the stories themselves are very deep and can be interpreted many ways:
* Both are thought-provoking about the world around us - as in which kind of present and future we want to live in?
* Female leads appear to be something beyond normal human, or at least, regarded as such.
Anyways, in terms of depth these series both have it. That is if you are looking for something in that regard.