In the “Class of …” series, Nick Rogers takes a monthly look back at films celebrating either their 20th or 30th anniversary of initial release this year — six from 1994 and six from 1984. The rules: No Oscar nominees and no films among either year’s top-10 grossers.

Predating a late-’80s surfeit of body-swap comedies that were either terrific (Big) or terrible (18 Again), All of Me splendidly speculates what might happen when two antagonistic souls scramble for control of the same body. And although All of Me hit theaters just three decades ago, its soul feels much older — which is to say more witty and wise than wacky or woolly.

Under director Carl Reiner’s devilishly deft vaudevillian touch, this is 1944 by way of 1984 — with irresistibly farcical forward momentum, a dollop of PG-rated dirty talk, wickedly smart one-liners, sophisticated slapstick and just the right pinch of sadness. (Based on Me Two, a novel by Edwin Davis, the snappy script comes from Phil Alden Robinson, who made the Best Picture nominee Field of Dreams just five years later.) But All of Me’s true timelessness emanates from Steve Martin — who discovered a critical moment of career maturation in his fourth film with Reiner.

By 1984, Martin was a long-bankable stand-up comedian, writer, Saturday Night Live host and purveyor of big-screen silliness (The Jerk, also directed by Reiner). But his attempts, however acclaimed, at musical drama (Pennies From Heaven), genre parody (Dead Men Don’t Wear Plaid and The Man with Two Brains, again by Reiner) and romantic comedy (The Lonely Guy) were box-office duds. Indeed, All of Me’s old-fashioned style brought out something new in Martin, even if he still did the funny voices.

Here, Martin offers a master class in physical comedy (more on that in a bit). Also, for the first time, he displayed the game-for-everything gusto to show he, like contemporary Robin Williams, could modulate mania into something warmer, longing, human. Without All of Me, there is no Roxanne, Planes, Trains and Automobiles, Parenthood or L.A. Story.

Martin’s turn earned him a Golden Globe nomination and Best Actor awards from both the National Society of Film Critics and the New York Film Critics Circle (which hasn’t since feted such a full-fledged comedic performance in the category). With that cachet, you’d think Martin might have been among the few comedians to earn Oscar attention for a (more or less) funny role. But he was likely unseated by either dual nominations from that year’s Best Picture winner, Amadeus, or the Academy’s unwillingness to allow two black-swan aberrations, given the rare sci-fi performance nomination for Jeff Bridges in Starman.

Martin plays Roger Cobb, a slave-away attorney whose true love is jumping onstage to play jazz guitar every night after a long day at the office. These passions pull him in two directions. But staring down 40, though, Roger ultimately chooses comfort, convention and convenience. (“I’m dedicating myself to a full-time legal career,” he quips. “Later today, I’m buying a vest.”) He’s cohabitating (joylessly) with the boss’s daughter (Madolyn Smith) and chasing a partnership by representing said boss (a perfectly oily Dana Elcar) in his divorce trial; it seems he’s become “the West Coast distributor of love and happiness” to every woman except the one he married.

The boss also hands him a cash-cow case: Handling the estate of soon-to-be-dead millionaire heiress Edwina Cutwater (Lily Tomlin), from which the law firm can leach for years. Edwina’s plans to cast off her childhood pall never came to pass. Bedridden nearly her whole life, she surrounds herself with sycophants in a well-appointed mausoleum masquerading as a mansion. (If the joint looks familiar, that’s because it would later belong to the other Jeffrey Lebowski in The Big Lebowski.) Edwina’s tact is just as decrepit as her body, as she constantly harangues Roger’s working-man ethic.

“Because I’m rich,” as she says, Edwina is funding an incredulous idea to live a life she’s always dreamt of, even after her death. Aided by wide-eyed mystic Prahka Lasa (Richard Libertini), she’ll transplant her soul into the young, healthy stable master’s daughter, Terry (Victoria Tennant, whom Martin later married and co-starred with in “L.A. Story”). But before Edwina dies, she needs Roger to bequeath her vast fortune to Terry. Roger scoffs at the endeavor as a wasteful scam. She figures if money can’t help her in this life, it might as well help her in the next one.

Martin and Tomlin lend brisk, aerodynamic zing to their contentious class-warfare lobs. Eventually, though, these ideological antagonists have to join forces. Edwina’s plan works, but sends her into the wrong body: Roger’s. Once there, she takes control of his body’s right side and projects her thoughts into his head. Together, they must track down Prahka, try to win the divorce case and undo Terry’s conniving plans before they’re forever stuck in the same body.

All of Me is blessedly light on dated visual effects, relying instead on clever use of “mirrors” to keep Tomlin around. And even if an eventual romance feels a little less than convincing (and their seeming inability to simply visit Prahka’s hotel room a nagging irritant), All of Me is a spry, wry treat elevated by two legacy comedians.

Tomlin, who also earned a Golden Globe nomination, effortlessly delivers on withering Ernestine-esque wit but also excels at the exhilaration Edwina feels, even in the wrong body. However ill-equipped (plenty of chaste penis jokes), Roger’s is the only healthy human form she’s ever inhabited. And there’s even a somber subtext to All of Me’s more ribald moments, namely when Terry seduces Roger. For him, it’s a trophy-prize romp. For Edwina, it’s spiritual virginity she’d rather not give it up lightly.

All of Me is careful and considerate enough to establish that there are chinks in Roger and Edwina’s emotional armor with which they deflect misery. And when both of them cut loose in a dance at the end, there’s an exuberance in the way they spin and grin goofily.

For all of its revelry in the ridiculousness of the plot to rid Roger’s body of Edwina, All of Me is about two people rediscovering consciences and compassions that have been cooped up far too long. Unsurprisingly, such a ripe high-concept comedy is on the roster of remakes. Attaching the writers of He’s Just Not That Into You and Valentine’s Day, however, is a dispiriting prospect.

Whatever form the remake takes (if it even happens), woe unto the poor bastard who has to follow in Martin’s footsteps. Here, he’s given the rare opportunity to play straight man and screwball, often switching back and forth in a matter of seconds. And although Martin is generally much less regarded for his physical comedy skills than greats like Lloyd, Keaton or Chaplin … well, I’d argue he reaches that rarefied air here. Others would, and have, overindulged the wobbling legs or overplayed the “split-personality” conversations. But this is no mere frenzy of flailed limbs or comically cuckoo calisthenics. Martin treats Roger’s manic movement as a precise manifestation of two characters from which uproarious laughs naturally flow.

When Edwina enters Roger’s body, Martin infuses the incident with physical heft and existential panic. Simply through the suggestive power of how he positions his limbs, Martin makes it seem Roger is pushing back against an immovable cosmic force just trying to walk. He’s subtle enough to understand the connotations — and, in his furrowed brow, the grave concerns — of the circumstance in which Roger finds himself. Martin also specifically establishes Roger’s new metaphysical meridian, sashaying on the right and straight-leg walking on the left. Then there’s the precision placement of “Edwina’s” right hand, daintily leaned out as though against an invisible ledge, knuckles curved and wrists flicked just so. Even Martin’s hair, perfectly tousled, feels like an extension of Roger’s frazzled nerves.

Martin is not trying to be wild and crazy in the way, say, Jim Carrey is during similar moments in Liar Liar. (And Martin elevates this film’s courtroom scenes to even more mindboggling meta-textual levels. When Roger “falls asleep” during the divorce case, Edwina must pick up the slack — thus, a man playing a woman interpreting a man.)

Over the last decade or so, it’s been easy to lose sight of Martin’s gifts amid flabby remakes (Cheaper by the Dozen and The Pink Panther), cash-hungry sequels to said remakes or condescending crowd-pleasers (Bringing Down the House). But the flickers of his fulsome gifts are there in Baby Mama and It’s Complicated. And whenever you might doubt it most, All of Me serves up timeless, indelible, irrefutable proof: Martin is not just among the funniest men alive. He’s one of the most thoughtfully funny men alive.