Times Square isn’t the only place where theatergoers will be able to stargaze this fall: Adam Driver, Kenneth Branagh, and Kate Mulgrew are among the stage and screen veterans poised to appear off-Broadway in shows ranging from revivals and new adaptations of classic works to original plays and musicals, touching on subjects ranging from the Arab Spring to our fast-approaching presidential election.

Vladimir Putin, vaccine mandates, and robots are among other diverse influences on a field that’s far too crowded to acknowledge in full. Our critic offers a selective guide, with brief descriptions of upcoming productions that have piqued her interest — including a couple she’s eager to see for a second time. (Dates and other details are subject to change.)

‘Table 17’
Kara Young, a Tony Award winner for her luminous performance in last season’s Broadway revival of “Purlie Victorious,” stars in a new romantic comedy by the playwright behind “Chicken & Biscuits,” Douglas Lyons, focusing on a formerly engaged couple. (In previews, opens September 6)

‘See What I Wanna See’
A new staging of the Michael John LaChiusa musical, based on short stories by author Ryūnosuke Akutagawa, features an all-Asian American and Pacific Islander cast, with director Emilio Ramos drawing on traditional Asian theater practices. (Previews begin September 3, opens September 16)

‘Ghost of John McCain’
Donald Trump and his brain are separate roles in a new musical, in which numerous other recognizable characters appear in addition to McCain, including Joe Biden, Barack Obama, Hillary Clinton, Sarah Palin, Eva Perón, Kanye West, and Taylor Swift. Also recently added: Kamala Harris. (September 3, September 24)

‘Counting and Cracking’
The writer and director S. Shakthidharan digs into his family background for a multilingual epic — staged in English, Tamil, and Sinhalese — tracing a Sri Lankan-Australian clan over nearly five decades, beginning in 1954. Eamon Flack directs. (September 6, September 12)

‘The Beacon’
Kate Mulgrew returns to the stage as a distinguished artist with a shady past in this North American premiere of a work by an Irish playwright and screenwriter, Nancy Harris, at Irish Repertory Theatre. (September 11, September 22)

‘Medea: Re-Versed’
Euripides gets a hip-hop spin in a new adaptation of the Greek tragedy, crafted in battle rap verse by playwright and composer Luis Quintero, who will also serve as Emcee. (September 12, September 23)

‘Our Class’
Tadeusz Słobodzianek’s beautiful, harrowing study, adapted by Norman Allen, of 10 Polish classmates — five Jewish, five Catholic — through the Holocaust and subsequent decades transfers to Classic Stage Company following a run at the Brooklyn Academy of Music last winter. (September 12, September 17)

‘The Big Gay Jamboree’
A co-creator and star of the off-Broadway sensation “Titanique,” Marla Mindelle, is back in “a new comedy trapped inside a musical,” written by Ms. Mindelle with Jonathan Parks-Ramage and Philip Drennen. (September 14, October 1)

‘Safety Not Guaranteed’
In a new musical inspired by the 2012 film, having its world premiere at BAM, a journalist looks into a classified ad seeking a time-travel companion. Ryan Miller, frontman of a popular alt-rock group, Guster, wrote the music and lyrics. (September 17, October 3)

‘Good Bones’
Playwright James Ijames and director Saheem Ali return to the Public Theater, where they last collaborated on the Pulitzer Prize-winning “Fat Ham,” with a new work, about a woman who gets more than she bargains for when she and her husband set out to renovate a house in her old neighborhood. (September 19, October 1)

‘The Counter’
Anthony Edwards, Susannah Flood, and Amy Warren are guided by celebrated director (and actor) David Cromer in the world premiere of a play by Meghan Kennedy, following a waitress in a small-town diner and one of her regular customers. (September 19, October 9)

‘Vladimir’
Another acclaimed veteran, Daniel Sullivan, directs another world premiere, of a play by Erika Sheffer; set at Moscow and featuring a two-time Tony winner, Norbert Leo Butz, it’s centered on an independent journalist covering Vladimir Putin’s first term. (September 24, October 16)

‘Hold On to Me Darling’
In a new production of the Kenneth Lonergan play directed by Neil Pepe, Adam Driver stars as a country music idol who suffers an existential crisis, and finds the simple life ain’t so simple. (September 24, October 16)

‘I’m Almost There’
Mr. Cromer directs performer, songwriter and playwright Todd Almond — in eight performances only — through a love story delivered in song, which arrives fresh from a well-received run at this year’s Edinburgh Fringe Festival. (September 26-October 5)

‘Bad Kreyol’
In the latest offering from the “Confederates” and “Skeleton Key” playwright, Dominique Morrisseau, a first-generation Haitian American travels to her ancestral homeland to reconnect with a cousin, leading both to face their different perspectives. (October 8, October 28)

‘We Live in Cairo’
New York Theatre Workshop presents a Richard Rodgers Award-winning musical by “Usual Suspects” (company-affiliated artists) Daniel and Patrick Lazour, inspired by the young Egyptians who became activists during the Arab Spring. (October 9, October 27)

‘Teeth’
This gleefully profane musical by a Tony and Pulitzer winner, Michael R. Jackson (“A Strange Loop”), and Anna K. Jacobs, inspired by the titular cult comedy-horror flick, is back after earning applause and guffaws — and no doubt a few shrieks — in a production last March. (October 16, October 31)

‘Walden’
A rising playwright, Amy Berryman, and an Obie Award-winning director, Whitney White, team up for a look at twin sisters, raised to be NASA scientists, who pursue different paths; a reunion triggers old conflicts. (October 16, November 7)

‘We Are Your Robots’
At Brooklyn’s Theatre For a New Audience, a Broadway vet, Leigh Silverman, directs a new musical written by and starring playwright and performer Ethan Lipton. Mr. Lipton and longtime bandmates and collaborating composers Vito Dieterle, Eben Levy, and Ian Riggs play the title characters, who are eager to know what humans want from them. (November 10, November 21)

‘King Lear’
Having already tackled Hamlet and Macbeth, Kenneth Branagh completes the tortured trifecta in a production he’ll also direct, along with Rob Ashford and Lucy Skilbeck. (October 26, November 14)

‘S—. Meet. Fan.’
An Obie winner, Robert O’Hara wrote and will direct the world premiere of a play based on the Italian film “Perfect Strangers,” tracing a group of old friends gathered on the night of an eclipse, as they pour cocktails and spill secrets. (October 10, October 28)

‘The Blood Quilt’
Lincoln Center Theater’s resident director, Lileana Blain-Cruz, helms a new play by a Pulitzer winner, Katori Hall, following four sisters reunited after their mother’s death. (October 30, November 21)

‘The Dead, 1904’
In 2016, Irish Rep revisited James Joyce’s novella for a much-loved immersive theater event. It returns just in time for the holiday season, to the American Irish Historical Society, where audiences of 48 people will be entertained nightly over three floors of a Fifth Avenue townhouse. (November 20, November 26)

‘The Merchant of Venice’
The “Our Class” director, Igor Golyak, has adapted Shakespeare’s sadly timely tragicomedy, and has cast members of that previous production, among them Alexandra Silber as Portia and Richard Topol as Shylock. (November 22, November 26)