Alec Baldwin didn’t realize that the joke would drag on this long. When he succumbed to the pestering of his buddies Lorne Michaels and Tina Fey and agreed in September to act as Donald Trump on Saturday Night Live, Baldwin figured that the role would be a short-lived, splashy cameo, like Larry David playing Bernie Sanders, or Fey impersonating Sarah Palin. And then Trump won. Neither the president-elect nor the man imitating him seems to have thought this far ahead.

The early days of Trump’s transition into office have been tumultuous and slapdash, marked by sudden releases of staffers and reported inquiries by Trump about just how much time he really has to spend in the White House. Baldwin, meanwhile, told WNYC’s Brian Lehrer on Election Day that he was “trying to shed the Donald Trump cloak,” and that his jaw was sore from mimicking Trump’s thrusting cadences. Baldwin did not appear on SNL’s first postelection episode, raising questions about who will play Trump going forward.

Over the last year, Trump has been portrayed on SNL by Baldwin; longtime impression impresario Darrell Hammond; and Taran Killam, whom the show let go this summer. (Back in the late ’80s and early ’90s, Phil Hartman’s Trump popped up from time to time, including alongside a young Fred Savage.) Whether Baldwin will return to the show in some capacity remains unclear, but it seems increasingly unlikely that he will handle the role on a long-term basis. Theories about who might take over have included Hammond, as always, as well as current SNL cast member Beck Bennett, who has played Mike Pence of late. Anthony Atamanuik, who is not a current cast member, also drew attention with his two-man show, Trump vs. Bernie, which toured earlier this year.

But none of these people should represent the president-elect on Saturday Night Live because addressing a candidate as problematic as Trump calls for an atypical solution. Trump may be the eighth president to serve during the show’s 42-season run, but he has already presented a unique challenge for not just SNL, but for parent company NBC. When Trump was still just a candidate to win the GOP nomination, the network claimed that it had severed ties with him on Celebrity Apprentice and other programs based on racially charged comments he had made. A few months later, SNL asked him to be a host, a decision that was roundly criticized. The misogynistic 2005 conversation between Trump and Billy Bush took place on an NBC lot.

The incoming president and his cronies say and do things that are so shocking that they defy easy attempts at laughs. (When someone’s supporters are bringing up World War II internment camps with implied approval, what’s the point of reminding everyone that Trump has silly hair?) SNL is certainly an obvious part of the coastal liberal self-congratulatory media conglomerate that Trump has successfully railed against, which makes reacting to him tricky: Just about anything can be replied to with an unassailable “Well yeah, you would say that!” Being too neutral, or too gentle, or even too funny can run the risk of softening up a man who has said and done some truly disturbing things for much of his life.

As for any company that wins important business, the best answer to all of this is for SNL to put its top people on the account. And in this case, the top person is cast member Kate McKinnon, now in her sixth season. The recent Emmy winner elevated the character of Hillary Clinton throughout the campaign and has emerged as one of SNL’s most compelling talents. She is a seriously outlandish comedian who is perfectly positioned to take on the season’s most important role: Donald Trump.

This summer, McKinnon spoke with The New York Times’ Dave Itzkoff about her work in the movie Ghostbusters and her role as Clinton on SNL. McKinnon continually downplayed her influence throughout their chat. “I look at a politician or a scientist and think, they’re creating the content of humanity,” she said. “I can’t believe I get to even comment on this in some small way. … Comedy has become, I think, a very important branch of public intellectualism. But it still ain’t Washington.”

McKinnon is one of the most exciting comedic actors in years, a captivating on-screen force with an elastic pelvis and a deadpan drawl. She has the abandon of Kristen Wiig but with more of an edge; the outrageous range of Mike Myers but with less of the drama. She can nail Justin Bieber and Ruth Bader Ginsburg and completely out-Ellen Ellen. Her first-ever appearance on SNL was pretty much flawless, while her best-ever sketch was so utterly (and udderly?) creepy that Ryan Gosling only barely survived.

Many hilarious women have played Hillary Clinton on SNL over the years — including the great Amy Poehler, with her perfect mirthless laugh — but McKinnon’s version of the role has been the finest: tightly wound but wacky, erratic but indulged, a study in political ensconcement. “I spend so many hours studying her and imagining her inner life,” McKinnon told Itzkoff, “that I feel like we’re very close. Even though I don’t have her phone number.”

Writing for The New Yorker in April 2015, shortly after Clinton announced her candidacy for president, Ian Crouch described McKinnon’s Hillary as “a performance that builds on a studied impersonation to become a singular new character” and hailed the likeness as “already among the best impersonations of a politician ever to appear on the show — joining a list of greats that includes Dana Carvey as George H. W. Bush, Phil Hartman and Darrell Hammond as Bill Clinton, Will Ferrell as George W. Bush, and Tina Fey as Sarah Palin.”

In September, McKinnon earned an Emmy for outstanding supporting actress in a comedy series based on her suite of characters, Clinton included. A Clinton win on Election Day would have pushed McKinnon further into the popular consciousness. And it’s something she was also hoping for on a personal level: McKinnon held back tears when she talked to Rolling Stone earlier this fall about imagining a female president. It’s likely that she, and SNL generally, figured this winning bit as Hillary would last for years. And then Trump won, so it won’t. But that doesn’t mean her political contributions should end there.

Figuring out how to tackle Trump must feel like a particularly fraught decision for SNL. He ran a campaign that was simultaneously rife with comedic material — never forget that he brought up a years-old beef with Rosie O’Donnell unsolicited in the closing minutes of a presidential debate — and deadly fucking unfunny. For the better part of two years, Trump cynically and deliberately riled up his supporters with messages of belittlement and bigotry. He is currently cobbling together a frightening assemblage of ghoulish, paranoid cast-offs to run the country in his stead.

“Very organized process taking place as I decide on Cabinet and many other positions,” Trump tweeted Tuesday night, in response to various reports about the disarray surrounding his transitional administration. “I am the only one who knows who the finalists are!” It’s hard to outdo a narcissist who is already such an able parody of himself. “What makes Trump ridiculous and grotesque,” wrote Slate’s Willa Paskin, “is also what Trump loves about himself, and this has made him difficult to properly satirize.”

It also, for a long time, made him easy for many to take lightly. The Huffington Post infamously filed all Trump news under Entertainment, and not Politics, for nearly half of 2015. (They ceased with the gimmick once he called for a “total and complete shutdown of Muslims entering the United States.”) Jimmy Fallon, who has sported a Trump wig in the past, tousled the man’s actual hair on late-night TV, to universal thumbs down. Late last week, People ran an adoring cover of the new president-elect — weeks after one of its former staffers, Natasha Stoynoff, wrote a detailed piece accusing Trump of sexually harassing her as she reported on him more than a decade ago.

Trump is a keen showman and self-promoter who finagled all sorts of free airtime over the past 18 or so months thanks to his steady supply of provocative statements, offensive lies, and mind games with the media. Which is why he was all too happy to host SNL last year. For some viewers, though, Trump didn’t even have to be hosting for the program to still feel somehow complicit in advancing a more palatable version of him to the world. His being a character was enough.

Last week, R.E.M.’s Michael Stipe was a guest on Baldwin’s WNYC radio show. (Amusingly, when Fallon was a guest on the program last December, the title was: “Jimmy Fallon Will Never Make Fun of You.”) “It’s so sad that we have allowed ourselves to sink to this level of, really, entertainment, that’s what it is,” Stipe said of the environment surrounding the election. “And I blame media completely for it — including Saturday Night Live, sorry to say.” To which Baldwin replied: “Lay it on me, baby.”

“What does it feel like from inside?” Stipe asked. “What does it feel like playing that character? It’s satire, brilliantly done — but it’s adding to the push of — Andy Warhol said, ‘There’s no such thing as bad publicity.’ How have we created this monster? How have we put our particular American brand onto this thing?”

The most effective satire has a point of view and makes a point. It wields humor like a scalpel, slicing clean and deep through layers of increasing resistance to expose the bone. Often, as in Saturday Night Live, much of it is delivered in the form of an impersonation. But as Slate’s Jacob Rubin wrote in March 2015, in a celebration of Dana Carvey’s George H. W. Bush, “the best impressions … almost always fail as satire” because “the intended skewering is set off by the very humanizing attention that makes the impression great.”

Will Ferrell’s Dubya — who batted around toys like a kitten and butchered words with childlike wonder — was a brilliantly conceived performance that has grown increasingly indistinguishable from Bush himself as time has gone by. But while the character’s “inner boy [kept] breaking free of propriety’s straightjacket,” as Rubin put it, the actual president was a vastly unpopular grown man who started wars. In a Saturday Night Live documentary, Ferrell said that his portrayal may have ultimately endeared Bush to some people, while a 2003 Esquire profile of Karl Rove noted that “strategery” — a butchered Bushism that Ferrell coined — was eventually reclaimed by White House staff as a badge of pride.

In an episode of his Revisionist History podcast called “The Satire Paradox,” Malcolm Gladwell explored these sorts of potential pitfalls by looking at work ranging from Margaret Thatcher’s England to Stephen Colbert’s former greenroom to Palin’s Alaska. Referring to an interview between Fey and David Letterman in which the two discussed the influences behind Fey’s accent during her smash-hit Palin impersonation, Gladwell got worked up.

“They want the laugh,” he said, “so they make fun of the way she talks. But the way she talks is not the problem!” He went on to complain: “You’re left with one of the most charming and winning and hilarious comics of her generation letting her charisma wash over her ostensible target.”

Baldwin’s version of Trump was strikingly on-point physically. “The wig looked good,” wrote The New Yorker’s Crouch. “The skin tone was spot on. The voice sounded right. Baldwin’s resting face was a bit more scowly than Trump’s, but he nailed his lumbering gait and uncomfortable stoop at the lectern, as well as his penchant for interrupting.” It was, Crouch wrote, “a blustery performer playing an even more blustery real-life character.”

But in much the same way that the defeated Democrats will need to reimagine, on a macro level, their strategy going forward, Saturday Night Live would be smart to adjust this sort of bread-and-butter approach. Trump’s wispy hair and puckered lips, to paraphrase Gladwell, are not the problem. Playing Trump as a standard-issue windbag carries the danger of injecting collateral gravitas into the man.

One option would be for SNL to have no one play him, to focus instead on all the slimy characters in his immediate swamp: his sons; Steve Bannon; Rudy Giuliani; the ruthless Ivanka and her vengeful husband, Jared; Paul Ryan and Mike Pence. The joke could be that the unseen Trump is nothing but their puppet, that his life these days is just a series of people scheming behind his back whenever he leaves a room. (Sad!)

But that probably lets him off too easy. The most damning attempt at skewering Trump that I’ve seen to date was an offhand impression that Carvey whipped out on Conan back in June. Rather than give Trump a blowhard New York accent, Carvey spoke in a dopier, higher-pitched octave punctuated by “terrifics” that made Trump sound like a combination of a singing Chipmunk and Eric Cartman yelling, “Screw you guys, I’m goin’ home.” Stripped of bluster, the effect was part slick-talking, snake-oil salesman, part snake.

McKinnon could ably plumb those depths. She wouldn’t have to impersonate Trump — although hey, some of those blobfish prosthetics might not hurt — she’d just have to channel him, to embody his many insecurities and call out his tells and use them all to make a point about his base motivations. This is what made her such a rich and nuanced (and funny) Hillary Clinton, and it’s what could make her an impactful Donald Trump.

“I try to have a bit of swagger,” she told Rolling Stone, “but I have what my friends call Ratatouille hands … I’m a small woman. So that juxtaposition of two disparate traits is something I relate to deeply — and I think it’s the essence of any comedic character.” Having a woman — the most qualified woman, no less — play the next president would be a compelling decision after this particular election, and what’s more: It would most likely drive the real Trump, tiny appendages and all, nuts in a genuinely meaningful way.

There are potential pitfalls to giving McKinnon this assignment, to having such a divine comic talent associated with such an unusually toxic role. Like Ferrell with Bush, there’s the risk that she’s too good: that she makes people forget about the person Trump has revealed himself to be, that people’s true horror is obscured or ignored by the punch lines. And there’s the unsettling possibility that McKinnon would be targeted by Trump supporters who don’t find any of it funny — or would be targeted by the future president himself.

But figuring out how to properly engage and grapple with a force like Trump is, for a show like SNL, one of the most important assignments to ever come along. And so shouldn’t the show’s biggest talent be the one to take a crack? McKinnon may have been wrong when she allowed herself to think about playing the role of the first female president, but that doesn’t mean she can’t still play the commander-in-chief in a slightly different, and ultimately higher-stakes, way. And even if the powers that be at 30 Rock have something more standard in mind for Trump, don’t count out McKinnon just yet. She’d also make a terrific, just terrific, Steve Bannon.