 If you liked
Full Moon wo Sagashite
|
 ...then you might like
Kirarin☆Revolution
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Kirarin Revolution and Full Moon wo Sagashite are about a girl becoming an idol and learning about show business through their career. There's romance, some rivalry, a campaign between the main character and their rival that ends up as a competition, and a cat that follows the main character around. Full Moon is more darker than Kirarin, though.