I see romance manga with couples breaking up & getting back together all the time, but are there any where the character already starts out broken up, and the whole story is about him/her reconciling with his/her ex?

Maybe the protagonist was a cheater/player, and soon realized the error of his/her ways? The classic "MISUNDERSTANDINGS" break-up? At any rate, I am interested in looking into some manga where the protagonist is pursuing his ex. Not a new relationship, but rekindling an old one.

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If I've made a thread in the "I'm Looking For..." forum, I am only interested in Japanese manga. I am not interested in non-Japanese media at this time.

Jounetsu no Hate ni
Emma to Hakushaku
Kaze no Uta o Kike
Akunaki Jounetsu
Fujitsu na Koibito
Graecia no Mahou
Judar no Oukan - Senichiya ni Oborete
Omokage o Motomete
Ososugita Saikai
Pride to Ai to
Saikai wa Nigaku, Ai wa...
Sheikh ni Sarawarete
Sicilia de Aishite
Ubareta Hanayome
Youfu o Enjite
Zankoku na Sankoku
Those are all Harlequin based. Not sure if you're into them, or already read them, but all of them start with ex's getting back in the other's life and reconciling.
I hope you enjoy them. (There's probably 3-4 I missed, but if you really want them, I'll look for them ... maybe ... if I'm not lazy ... )

I'm drawing a blank for anything not Harlequin based ...

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Boku to Watashi no Henai Jijou - The couple breaks up on the first page, then the rest of the manga is about them getting back together. They don't break up due to a misunderstanding though.

piece somewhat fits? only they were never really together, but liked each other