So... is MM! finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: December 18, 2010
Manga finished: February 27, 2012
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
MM! follows Taro Sado, a high schooler struggling with his masochistic tendencies. He seeks help from the Second Voluntary Club to overcome this "problem."
However, Taro quickly discovers that the club members are far from ordinary. Each member, including the self-proclaimed god Mio, the androphobic Arashiko, and the sadistic Michiru, has their own unique and often bizarre issues.
As Taro and the club members interact with each other, along with other eccentric individuals like the massage expert Yumi and the inventive Noa, they embark on a journey of self-discovery and understanding. They learn valuable lessons about acceptance and the importance of kindness in their chaotic lives.