Total Recommendations: 1
If you liked
Nisekoi
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...then you might like
Kakkou no Iinazuke
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Very similar anime. The protagonist accidentally meets a girl and later has to play her boyfriend because of their familys. While the reason for the engagement in "A Cuckoo Couple" was a mix-up in the protagonist's birth, in "Nisekoi" it is the enmity of both yakuza families. Both are great romcom harem anime shows and well worth checking out.