In his latest movie, “Marjorie Prime,” Jon Hamm plays a hologram who gives tender therapeutic advice to the aging lady he was once married to (it’s complicated), and if that doesn’t strike you as exciting, you’re not alone. The movie is a precious indie bauble that has already whiffed at the specialty box office. Hamm is crafty and spry in it; you might say — as some have — that it’s an adventurous role for him, in the same way that playing a violent sociopath with choppy shaved hair in “Baby Driver” was an adventurous role for him. These characters aren’t what we “expect” from Jon Hamm, so they make it look like he’s in there, trying on audacious things and working it. The question is: Why does Jon Hamm now look like he’s trying so hard?

I think what I’m asking is: Why isn’t Jon Hamm a movie star? It’s an awkward question to pose, because we all know the entertainment industry doesn’t mint movie stars the way it once used to. It now mints franchises that are bigger than any one star. Beyond that, Jon Hamm’s image as an actor rests on a television series that, as much as any series in the history of the medium, proved that television could vibrate with an artistic electricity heady and bold enough to rival that of any contemporary movie. To presume that Hamm, after “Mad Men” (which ended in 2015), should have “graduated” to the movies may sound like outdated or even patronizing thinking.

Yet let’s be honest: If you compare him to the two other greatest actors of the new golden age of television, Bryan Cranston and the late James Gandolfini, Hamm, on “Mad Men,” had a tall-dark-and-handsome sharky elegance combined with a glamorous film-noir danger that made him seem, uniquely, like the 21st-century version of a classic movie star (think Robert Mitchum with a touch of Gregory Peck).

His look alone — the inky perfect hair, the thrusting chin and reluctant smile, the killer eyes that could melt or freeze you — was worthy of 007. Beyond that, Hamm inhabited Don Draper’s slithery soul in a way that invited the audience into a fascinating complicity with him. Over those years, I read a lot of great “Mad Men” recaps, but a blind spot shared by more than a few of them was the tendency to judge Don’s sins from on high, and to presume that the show viewed his hungry and often illicit soul with that same moralistic detachment. I’d argue that the ambiguous glory of “Mad Men” was how much it submerged the audience in Don’s point-of-view, and it was Hamm’s sonorous force as an actor that allowed that.

It’s that force that’s been waiting to be unleashed, to find a role — a great role — ever since the show ended. We now inhabit a culture so fickle that there are those who would write off Hamm as a one-hit wonder. (I expect to read a comment to that effect within 10 minutes of this column being posted.) But I don’t buy it. Hamm will be a true star again. In the years since “Mad Men,” however, it’s become more and more apparent why he’s fumbling around in movies that aren’t worthy of him.

He is, for one, a grown-up actor in a universe that’s increasingly kiddiefied; almost surely, he would have done better several decades ago. Yet Hamm’s biggest sticking point in terms of casting is tied to the very quality that made him so enthralling on “Mad Men”: He’s a victim of Intellectual Actor Syndrome. For all his swarthy allure, he’s an intensely brainy and articulate actor who leads, in spirit, from the neck up, and whose excitement and danger reside in his thoughts. That requires a script that can channel, through words, the actor’s energized quality of mind. Without it, he comes off as a ghost of himself.

Hamm seemed to get off to a good start on the big screen, giving an ace performance as the FBI Special Agent on the tail of the Fenway Park heist plotters in Ben Affleck’s “The Town,” which was released in 2010, during the height of “Mad Men” mania. But in the cause of “stretching,” he has made a number of bad choices, taking on roles that detracted from his mystique — like the part of Allen Ginsberg’s defense attorney in “Howl” (not a bad role, but the movie was too scrubby and earnest), or the fish-out-of-water sports agent who journeys to India to find a superstar pitcher in Disney’s innocuously inspirational “Million Dollar Arm.” There’s a value to not being overexposed, and Hamm, by saying yes to routine movies like these, made himself seem common, a gun-for-hire, part of the general scenery. I realize that actors have to work, but if the roles you choose end up dulling your brand, then they may not be worth the price.

Hamm has begun to seem like a supporting guy on the fringes, when what he really needs is a daring part that places him at the dead center of the action, a role built around his cutthroat fluency. Sure, you can’t cast somebody who looks like Jon Hamm as just anybody, but off the top of my head, I can think of any number of characters that he’d be perfect for.

It’s easy to imagine him taking on the Henry Fonda role of the U.S. president who goes through the negotiation of his life in a remake of “Fail Safe” (1964), Sidney Lumet’s great countdown-to-oblivion thriller, tailored to these neo-nuclear times. Or playing the shady hero of one of Woody Allen’s serious dramas about an ordinary man caught in a dark web of his own devising (“Match Point,” “Crimes and Misdemeanors”). And while some will surely say that Hamm, at 46, is too old for the part, I say: Cast him as Superman! Why not have the Man of Steel be a man instead of an overgrown pin-up, especially given that Henry Cavill has about one-ten-thousandth the charisma?

You should never give up the hope that Hollywood will make a romantic comedy for adults, and wouldn’t it be enticing to see Hamm star in one of them opposite an actress like Cate Blanchett? The sparks, and wit, could fly. Can Hamm sing and dance? He’s been brilliantly funny, and shown an effortless light touch, on “Saturday Night Live,” so I’m betting that he might have the talent to hold down a contempo post-“La La Land” musical. And there’s a juicy biopic that should really have his name on it: a movie about the wild, sordid, besotted life — especially the later years — of Errol Flynn. (There’s a Flynn movie in the works, but it’s an “action-adventure” that takes off from an episode in Flynn’s youth, leaving room for a much deeper dive into who he was as a star.) Also, this will probably sound insane, but I think Hamm would be an inspired choice to play Frank Zappa.

How do you land a role of ambition and audacity and white-hot buzz? After “Mad Men,” Jon Hamm should have had the world eating out of his hand. In the two years since, he has squandered some of that capital, but even so, there has to be a daring director out there — David O. Russell? Kathryn Bigelow? Paul Thomas Anderson? — who would kill to create a perfect role for him.

A character like Don Draper is, of course, a tough act to follow, and Hamm may be doing all he can to shake himself free of it, in the same way that Sean Connery, in the ’70s, went to elaborate lengths to shake himself free of James Bond. But Hamm would now do well to ponder the very qualities in himself that Don Draper brought out: the adman showmanship, the hound-dog cunning, the hint of mercilessness held behind a witty façade of civility. You can only play Don once, but Hamm, going forward, shouldn’t feel like he has to run from him. If he does, that may be an actor running from himself.