 If you liked
Full Moon wo Sagashite
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 ...then you might like
Bishoujo Senshi Sailor Moon: Sailor Stars
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The same maho-shoujo style and quite similar plot:
- the heroine's beloved is somewhere far (namely in the USA) and they will meet each other someday;
- meanwhile another candidate for being beloved appeared (by the way both guys are singers ;))
The difference is in heroine's choice and plot variations. Watch both: the feeling is pretty the same.