Almost two decades ago, in his one-man show “Laugh Whore,” the actor-comedian Mario Cantone recalled his struggles trying to inject life into Public Theater revivals of Shakespeare, playing the comic foil Stephano opposite Patrick Stewart’s Prospero in “The Tempest.” It did not go well, and Cantone vowed never to play Shakespeare again. “These are 400-year-old jokes,” he lamented. “You make them funny!”

The Bard’s comedies remain a challenge — for modern theater-makers as well as audiences. In recent years, though, the Public Theater has had considerable success paring down these problematic shows into one-act musicals. Nearly a decade ago, “Love’s Labour’s Lost” got an antic and tuneful contemporary update from director Alex Timbers and composer Michael Feldman. And in 2018, Kwame Kwei-Armah and Shaina Taub collaborated on a fleet-of-foot musical reimagining of “Twelfth Night” that hit a lot of high notes (and featured a star turn from Nikki M. James).

Now Taub has returned to the Public’s Shakespeare in the Park for a reworking of “As You Like It,” that chestnut about a young woman banished from her kingdom into the freewheeling Forest of Arden, where she courts her true love, a similarly banished young man, while disguised as a man. This being a Shakespearean comedy, there are also parallel love stories, including two involving mostly comedic characters that Taub (as well as co-adapter and director Laurie Woolery) have reimagined as same-sex couples.

All these shenanigans build to a quadruple wedding that involves a stage rush of dozens of ensemble members, mostly amateurs from the city’s five boroughs who have been rehearsing as part of the Public Theater’s Public Works program (half perform each night). There are pros on stage, too, including Taub as the misanthropic Jaques as well as a kind of M.C. who bookends the show with a tune based on the play’s most famous aphorism: “All the world’s a stage.”

For the most part, it all works — though there are quite a few rough patches along the way. Taub does not seem tempted to explore the transgender inclinations of the the show’s heroine, Rosalind (Rebecca Naomi Jones, a strong singer who showed some vocal strain at the performance I saw), who butches herself up as Ganymede as she slyly pursues her crush, Orlando (Ato Blankson-Wood, a wide-eyed standout with a crystalline voice).

Taub has also written some lovely tunes that bring a modern sensibility to the creaky 17th-century plot, turning Orlando’s marriage proposal into a Boyz 2 Men-style boy-band ballad (including dancing backup singers and a rhinestone-encrusted microphone) and crafting a lovely tune where Rosalind-as-Ganymede pretends to be a woman so that Orlando can practice his courtship skills. “I’ll flirt with you one second, act like I don’t care the next; drop a breadcrumb I adore you, then ignore your text,” she sings. In tunes like these, you can see and hear the Shakespearean patterns reverberating through a more contemporary gaze.

Taub has also laden her score with several clunkers, including an ill-conceived country line dance and other songs that seem more like missed opportunities. And just as Cantone predicted, the show breaks down in the book scenes that more faithfully lean on the Bard’s original text — and all those 400-year-old jokes — as well as archaic tropes like the court clown Touchstone (Christopher R. Ramirez) that elicit more cringing than laughter.

Still, it must be said that Central Park is spectacularly well cast as the Forest of Arden.