Realistically, if you're going to exclude TV movies, animated films, stuff based on newspaper comic strips... how many theatrically released feature films have there been based on characters who were created in comic books? Answer is: a few dozen so the likelihood of one character being in a run of four is pretty small and, apart from Jackman and Reeve, you're unlikely to find another one.

Let's have a think:
Superman I-IV, Supergirl, Superman Returns (presumably we can't count the Kirk Alyn serial or the Mole Men TV lash-up)
Batman, Returns, Forever, And Robin, Catwoman, Begins, Dark Knight + the 1960s TV spin-off (presumably we can't count the serials)
Spider-Man I-III (can't count the Nicholas Hammond TV lash-ups)
X-Men I-III, Wolverine
Hulk I+II
Fantastic Four I+II
Hellboy I+II
Blade I-III
Iron Man
Howard the Duck
Daredevil, Elektra
Mystery Men
Tank Girl
Judge Dredd
Barb Wire
Men in Black I+II
Constantine
The Crow I+II (III+IV were DTV)
From Hell, League of XG, Watchmen, V for Vendetta
Swamp Thing I+II
Ghost Rider
Punisher x3
Spawn, Steel
TMNT I-III

There are a few more but that's the bulk of them and it's only 60 films. In the grand scheme of things, with the restrictions in place, this is a minute subgenre. And look: Supes, Bats and X-Men are the ONLY franchises to have made it to four theatrically released live-action features.

So the answer to the thread title is a very simple and obvious 'no'.

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