So... is Star Ocean EX finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 25, 2001
Manga finished: October 12, 2005
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
Star Ocean EX follows Claude, a space-faring officer, who unexpectedly finds himself stranded on a primitive world called Expel.
He soon encounters Rena, a local who believes him to be a prophesied hero.
Together, they embark on a journey to uncover the mysteries surrounding a strange meteorite, known as the Sorcery Globe, and the chaos it's unleashing across the planet.
Along the way, Claude and Rena gather allies and face challenges as they work to understand and resolve the issues caused by the meteorite.