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When “The Coast of Utopia” opened at Lincoln Center Theater this fall, the challenges of selling the mammoth production were almost as daunting as its staging.

Tom Stoppard’s drama about 19th century Russian intellectuals hardly screams sexy and accessible. Not to mention “Coast” is a cycle of three plays totaling more than eight hours in running time, with the trilogy rolling out incrementally over a six-month period.

But helped along by Stoppard’s name, a starry cast, and stellar reviews, “Coast” surprised even LCT with how well and how quickly it sold.

Which created a whole new set of challenges.

The recently announced nine-week extension involved hammering out deals with the huge cast of 45 actors, who appear in all three plays. That added another layer of complexity to the basic logistics of the endeavor, which sees three productions opening one by one until all three then play in repertory through the end of the run, now set for May 13.

Following the Nov. 27 opening of part one, “Voyage,” the second part, “Shipwreck,” opens Dec. 21, with the closing installment, “Salvage,” bowing Feb. 15. The sked requires not just the balancing of rehearsals for one part with perfs for another. In February, when all three shows are up and running in rep, the popularity of marathon performance days raises the specter of accommodating a 1,000-person audience for an entire day.

And there will be six more of those marathon days — Saturdays during which auds will arrive at 11 a.m. to see all three shows — thanks to the extension.

Prolonging the engagement while preserving the entire cast was particularly impressive given that the ensemble includes such name thesps as Billy Crudup, Ethan Hawke, Jennifer Ehle, Martha Plimpton, Amy Irving, Brian F. O’Byrne, Josh Hamilton and Richard Easton.

But juggling the availability of all those performers proved easier than it sounds. “The actors just love doing it,” says LCT a.d. Andre Bishop. “There’s huge enthusiasm.”

Salaries were negotiated for the extension to “near Broadway equivalency,” according to LCT exec producer Bernard Gersten. (As a nonprofit, LCT generally pays thesps less than the union standard required for commercial Rialto productions even though LCT’s Vivian Beaumont Theater, where “Utopia” is being staged, is officially a Broadway house.)

The original suggestion was to push the “Coast” run all the way through the end of June. That would allow the show to take advantage of potential buzz from the Tony Awards, being handed out June 10.

“The actors were a little bit gun-shy on that,” says Gersten. For now the run ends May 13, just before Tony noms are announced, although a further extension remains a possibility.

At the very least, the longer engagement will help keep “Utopia” in the minds of Tony voters. Unlike “Angels in America,” another multi-part legit production whose two plays came six months apart and were eligible for Tonys in two consecutive years, LCT is pushing for all three parts of “Utopia” to be considered together as one single production. That issue will be decided in the spring by the Tony Awards admin committee.

The extension also will help boost the theater’s earned income from “Coast,” since the three installments have fewer total playing weeks than three separate productions at the Beaumont normally would. Due to a rigorous sked that reduces the frequency of performances for one part to make time for rehearsals for another, many weeks in the first half of the run have fewer than the standard eight perfs.

“We were short on earned income, but we had accepted the consequence of it,” says Gersten. He also said that mounting the three-parter cost roughly the same as three separate plays — usually in the area of $2 million-$2.5 million.

But even Bishop and Gersten didn’t expect “Coast” to prove quite so popular.

They originally planned a top-heavy sked, with 55 perfs of “Voyage”; 34 of “Shipwreck,” and 27 of “Salvage.”

“We didn’t assume everyone would want to see all three,” Bishop admits, adding that they believed many theatergoers would come for the first part to get a taste, but would not necessarily want to commit to two further plays.

They also assumed no one would buy the marathons, which have a hefty top ticket price of $300.

“I was totally deluded,” Bishop says.

The marathons were the first to go. Most buyers purchased more than one show, and many bought all three, which meant that “Salvage,” with the fewest perfs, sold out first. (Tickets remain available, on a very limited basis, to the original runs of the first two parts.)

“What we have found is, the play is accessible,” Bishop says — despite the show’s potentially intimidating intellectual pedigree, which was further pumped up by a recent article in the New York Times recommending 11 history books to read in preparation for viewing “Coast.”

Stoppard sent a letter to the Times in response, encouraging auds to come as they are. “What kind of madman would write a play that requires the audience to read a dozen books in advance?” he wrote.

With auds flocking to the imminent marathons, LCT is still working out the logistics of those day-long events.

“How do you make feeding arrangements for a thousand people?” Gersten asks of the auds who will be spending a total of 12 hours at Lincoln Center.

For now, LCT is planning to beef up its concessions and to provide lists of nearby restaurants.

“Will audiences bring their own lunch and eat in the lobby?” Bishop wonders. “We don’t know.”

Meanwhile, the cavernous backstage space at the Beaumont will be full to bursting with scenic elements and hundreds of costumes. With 34 stagehands and a dozen on the hair and wardrobe crew joining the 45 thesps, traffic is heavy.

“This was difficult on every level,” Bishop says. “But it’s exhilarating.”

After “Coast” ends, the next scheduled offering at the Beaumont is the much-anticipated revival of “South Pacific,” directed by Bartlett Sher in spring 2008.

Before that, the theater will house a still-to-be-determined play in the fall.

“A very, very small play,” Bishop says.