Are there any manga out there where one artist's work shares similar themes, plots or genres with another (but with a different setting and a new set of characters)?.

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See ya!

Do you mean collaborations between authors or works that resemble other manga? Or sequels, maybe? Fushigi Yuugi: Genbu Kaiden might work.

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"If you think being eaten by a carnivorous tree is something that only happens to someone else, then think again."
--Shades of Grey, by Jasper Fforde

fairy tail is sorta like one piece...

apparently both the authors were influenced by akira toriyama

I heard of spiritual successors for games with the same company, but not manga. However starfield hit the only one I can think of. Fairy Tail is definately a spiritual successor of One Piece. They have the same feel, probably thanks to similar protagonists, themes, and plots.

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An instant or an eternity. Both are the same, in the passing of an instant lies the beauty of eternity.
-Ginen Shounen

Because I am a small man, my heart is moved by what's in front of my eyes, not by what the whole world needs.
-D.Gray-man

Might not what ur looking for but kannagi and kanpachi?

One piece - Dragon Ball with pirates
Naruto - Dragon Ball with ninjas
Bleach - Dragon Ball with spirits
Prince of Tennis - Dragon Ball with Tennis Balls

Gintama and Sket Dance, maybe?
The mangaka of Sket Dance used to be Sorachi-sensei's assistant, so you could see his influence on the manga.

Totally didn't see your title, but I agree with One Piece and Fairy Tail.

Every shounen with a previous shounen.
Every shoujo with a previous shoujo.

And well if you want a more elaborate response I sort of think that theme-wise Death Note and Code Geass (I know the last one is an anime but still) are pretty similar (hyper idealist guy got an incredible power and thinks he can change the world). But well, that's just to try a "deeper" analysis, since imho what liquorice said it's not so far from the truth, every shounen manga share the same themes, plots, plots device, structure in arcs, etc.



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What I like in Trivial Pursuit style. Pick your category:

Fairy Tail is more of a spiritual successor to Rave, which was written by the same author. Most of the characters in either manga has an equivalent character in the other, and one of characters from Rave is in Fairy Tail as a cameo.

one piece to me feels like the spiritual successor to Jungle King Tar-chan
the insane
you never know what the hell is going to happen next[you know its going to be stupid]...but you know its going to be awesome-feeling