 If you liked
Tsubasa: RESERVoir CHRoNiCLE
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 ...then you might like
Cosmo Familia*
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Both share world hopping journeys to save the world, super natural settings as well as cute art and cute character designs too.
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Recommended by Disapeared_Ghost
Cosmo Familia and Tsubasa Reservoir Chronicle are two manga series about the main character going through another world (more than one for Tsubasa's case) in order to search for something/someone. Both also touch on time, similar looking characters, magical pets, and (intense?) fighting scenes.