Really, Jason Schwartzman should be a bigger star. Part of the prolific Coppola clan and erstwhile creator of teen drama theme tunes, he made his screen acting debut in Wes Anderson’s Rushmore in 1998 – a start that most could only dream of – but apart from a continued presence in Anderson’s films, he’s failed to grab the lead roles that his performances deserve. His performance in Alex Ross Perry’s Listen Up Philip is one of his most critically acclaimed yet, but why has it taken him so long to get here from his debut nearly twenty years ago?

The signs were good. Not many people could hold their own opposite Bill Murray on their debut, and even fewer could do it with such precocious charm and confidence. His role as Max Fischer, a polymath child genius prematurely disaffected with the world, certainly helped establish that image and it’s one that he’s clung to – or that perhaps clung to him – in many of his later roles.

He followed this philosophical indie debut with a lead performance for a like-minded auteur, David O. Russell, in his state-of-the-nation screwball comedy I Heart Huckabees – although six years and a cluster of smaller roles separate these two landmarks. His performance and the film itself drew a more mixed reaction from critics and audiences than Rushmore, but it also marked him as a comic performer enamoured with the offbeat and highbrow.

In 2007 he delivered one of his biggest and most underrated lead roles as Jack in The Darjeeling Limited. Wes Anderson’s road/train movie doesn’t get a lot of attention compared to his other films, but it has a powerful spiritual element and a great dynamic full of tender bickering between the three brothers at the heart of the film: Jack, Francis (Owen Wilson) and Peter (Adrien Brody). It’s also the most beautiful of Anderson’s films, save for perhaps The Grand Budapest Hotel, but it relies on a more natural look and tone than his latest masterpiece. Schwartzman is in a familiar role as a heartbroken author, but he is also the most sympathetic he’s ever been on-screen, searching for happiness and understanding as he travels through India with his brothers.

Then came minor roles in Funny People, Fantastic Mr. Fox and Walk Hard: The Dewey Cox Story (a hilarious, uncredited cameo as Ringo Starr), before another great performance in Edgar Wright’s cult classic Scott Pilgrim vs. the World (2010). As Gideon Graves, record label boss and one of Ramona’s evil exes, he is the big bad of the film and it’s a role he attacks with relish. There’s no pressure to be at all pleasant or appealing and Schwartzman lets loose with a display of controlled, cocky cruelty, manipulating and teasing Scott (Michael Cera) for the sake of it.

Perhaps this consistent selection of similar roles has left Schwartzman pigeon-holed, as it’s a persona he’s never really shaken throughout the rest of his career. By now he’s comfortably mastered the portrayal of these obnoxious wits; talented and commanding, but well aware of it. His lead performance in Alex Ross Perry’s Listen Up Philip might be the most extreme example yet. He plays an acclaimed author, stuck in a rut after his first novel, who falls under the wing of the legendary writer Ike Zimmerman (Jonathan Pryce). Like many of his previous roles, his character is bluntly honest, and it’s a trait that’s never been funnier. Zimmerman claims that Philip is “selfish and unsentimental” and in reply Philip only grins behind his shades and replies: “you say that like it’s a bad thing”.

He’s the kind of character you love to hate; the kind of person so ridiculous and self-absorbed that you struggle to imagine them existing in real life – except somewhere, in some vain, desperate upper-class ghetto they’re probably ten-a-penny. It makes for a performance that is easy to laugh at, but hard to sympathise with. It’s a theme common to most of Schwartzman’s roles and it might be the thing that’s holding him back from pushing him on to the next level as an actor. His performances are reliably excellent and always hilarious, but they’re almost too predictable and too extreme. He rarely plays someone believable or someone you could imagine being friends with.

It might be holding him back, but it’s not necessarily something you can imagine changing either. After all, who wants a bland, anodyne version of Jason Schwartzman? A big part of his appeal is in his larger-than-life characters who make an impression through their overwhelming mental rather than physical presence. If anything, Schwartzman just needs more roles, and bigger roles. He’s now an established part of the Wes Anderson travelling players, although another lead role from his long-time collaborator might be too much to expect. Maybe he’ll just continue to deliver great comedic supporting performances – and there are far worse fates than that. Comedy always suffers when it comes to critical acclaim, but he is undoubtedly at the top of his game in that genre. Or maybe he found the secret to acting happiness in his very first role: “The secret, I don’t know… I guess you’ve just gotta find something you love to do and then… do it for the rest of your life”.