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If you liked Shigofumi add

...then you might like Pandora Hearts add

When I was watching Pandora Hearts, the psychological aspects so far seemed similar to Shigofumi.

If you liked Death Note add

...then you might like Majin Tantei Nougami Neuro add

Although Neuro is a lot more light hearted, both animes have supernatural beings interacting (perhaps even manipulating) humans. Both are centered around murder mysteries, although Neuro is episodic (however, there is an overarching unsolved mystery in it too).