Robert Zuckerman/Walt Disney Pictures and Jerry Bruckheimer Films

“National Treasure”

Monday the Brattle starts a retrospective. It’s called Nicolas Cage: Greatest American Actor and runs through June 21.

Well, that’s one way of putting it. Another would be what one might call the Prince approach. Think of our subject as The Actor Formerly Known as Nicolas Cage.

Really, has any current star — maybe any star, period — had a stranger career? Not for Nic Cage any of the standard trajectories: not overnight success or flameout or comeback or slow fade into character parts or a Tom Hanksian steady-state stardom (definitely not that).

Nic Cage, Version 1.0., was all actorly devotion — Sean Pean with a darker complexion. He was brooding. He was intense. He was serious. He was all over-the-top commitment to his craft. How committed? Cage ate a cockroach onscreen in “Vampire’s Kiss” (actually, he ate three — one for each take). It plays Wednesday at the Brattle. Make sure your popcorn’s buttered.

Columbia Pictures

“Adaptation”

Cage is famously said to have had two teeth pulled for “Birdy,” to make his character look more haggard. Robert De Niro puts on 60 pounds to play Jake LaMotta, in “Raging Bull”? Christian Bale loses 55 pounds to play a POW, in “Rescue Dawn”? Fine. Let’s see if they’re willing to endure the dentist’s chair for their art. Now it’s true that reports differ on whether Cage actually had the extractions. The point isn’t whether or not he did. It’s that people believe he did. It just sounds like such a Nicolas Cage thing to do.

This stage of Cage’s career peaked with his Oscar-winning performance in “Leaving Las Vegas,” in 1996. Admittedly, it’s hard for an actor to top drinking himself to death onscreen. So, understandably enough, instead of trying to dig deeper, Cage started to set aside his shovel.

“Raising Arizona”

Nic Cage, Version 2.0, had its rollout with his next two movies: “The Rock” and “Con Air.” They play as a double bill in the series Saturday. In one of the more improbable transformations in Hollywood history, Nicolas Cage, post-Method seeker of emotional truth, had become Nicolas Cage, action hero. Soon enough there would be “Gone in 60 Seconds,” the “National Treasure” movies, “Ghost Rider,” “Bangkok Dangerous,” “The Sorcerer’s Apprentice.” Over the past 15 years or so, he’s gone from steak tartare to beef jerky, with a big helping of ham on the side.

Things have reached such a pass that Cage was in no fewer than five movies released last year. Don’t feel bad if you can’t name any. “Season of the Witch,” “Drive Angry,” “Seeking Justice,” “Trespass,” and “Ghost Rider: Spirit of Vengeance” didn’t exactly alter the face of film history. The man may have stopped working hard, but he certainly works.

In fairness, there has been the occasional return to 1.0 in the 2.0 era. There were the double-role movies, “Face/Off” and “Adaptation.” The former plays next Sunday, the latter on June 19. Cage has worked with Brian De Palma (“Snake Eyes”); Martin Scorsese (“Bringing Out the Dead,” a very Nic Cage sort of title); Oliver Stone (“World Trade Center”); and Werner Herzog (“Bad Lieutenant: Port of Call New Orleans.”) “Snake Eyes” plays next Sunday, and “Bad Lieutenant” plays June 21.

“Adaptation” brings up the great underutilized Cage resource: comedy. The hangdog face, the pained solemnity of the voice, the versatile hairline: They’re made for laughs. As “Nicolas Coppola” (Cage’s given name — Francis is his uncle), he made his feature film debut 20th-billed in “Fast Times at Ridgemont High.” Perhaps that particular film being his first was a portent of what might have been. Sure, Sean Penn won Oscars for his huffing-and-puffing in “Mystic River” and biopic nobility in “Milk.” But really, has he ever been better than as the blissfully oblivious Jeff Spicoli in “Fast Times’’?

So, too, with the Nic-ster. Monday showcases the comic Cage, with “Valley Girl” (no, he doesn’t play the title role) and “Raising Arizona.” He’s very funny in “Adaptation,” and in “Moonstruck” he may be the only romantic-comedy lead in film history with a wooden hand (another very Cage touch). “Honeymoon in Vegas,” where he and Sarah Jessica Parker make for a most improbable couple, can be seen as a welcome comic corrective to “Leaving Las Vegas.” Now that would be a double bill worth sinking your teeth into (so to speak).