 If you liked
Kamichama Karin
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 ...then you might like
Kamisama Hajimemashita
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Both are reverse harem-like around a little homeless goddess school-girl who needs protection:
Nanami=Karin (little goddess school girl)
Tomoe=Kazune (Romantic Interest #1/devoted-yet-prickly/classmate)
Kuruma=Ren (black haired singer/classmate)
Mizuki=Micchi
Aside from having similar characters---no, that's about it.
Kamisama is of the shrine-girl/traditional japanese kami type, while kamichama is a magic-girl time paradox issue.