NEW YORK — Tuesday night in New York City. Plenty of people at home watching nasty, naked coppers on ABC. Plenty of people on West 46th Street watching a Roman orgy of murder, mutilation and mayhem (call it “SPQR Blue”).It was something of a shock to arrive one recent weeknight at St. Clement’s, a venerable Off Broadway space in the heart of the theater district, to find Theater for a New Audience’s performance — indeed, its entire run — of “Titus Andronicus” completely sold out. True, it’s only a 150-seat venue. But this is a city that can turn a cold shoulder to the Royal Shakespeare Company and the National when those venerable companies venture across the pond, and “Titus Andronicus” isn’t exactly the best-known item in the Shakespeare canon. How, then, account for this anomalous success? Credit Jeffrey Horowitz, who founded Theater for a New Audience 15 years ago and has produceda remarkable range of Shakespeare and new plays. Directors have included such luminaries as the Royal Court Theater’s William Gaskill and the RSC’s Mark Rylance, as well as some of this country’s most brilliant young directing stars, among them Julie Taymor –”Titus” marks her third outing with the company — Elizabeth Swados and Amy Saltz. “Titus”– a remarkable production featuring Robert Stattel in the title role and Miriam Healy-Louie as Lavinia — is the company’s second show of the season, following Rylance’s acclaimed and equally adventurous staging in January of “As You Like It.” In addition, Theater for a New Audience commissioned Suzan Lori-Parks’ “The America Play,” produced with the Yale Repertory Theater and the New York Shakespeare Festival, where it closed this past weekend. Other works have been commissioned by the company from Swados, Darrah Cloud, Eduardo Machado , Ntozake Shange and other regulars on the resident theater circuit. The company runs lean on an annual budget of about $ 1 million, supported by public agencies, private foundations and a host of Broadway big shots. “I frankly don’t know how we’ve survived,” says Horowitz, a soft-spoken man with a mission. He founded Theater for a New Audience in 1979, but the dream had been with him for a decade, after three years in London. “That experience gave me certain models,” he recalls, “seeing these great state theaters with superb artists, being seen by diverse audiences. I saw Olivier for 60 cents. That’s what the ‘new’ in New Audience stands for: diverse in terms of economics, age, ethnicity. And I found I was more drawn to European theater, where metaphor was more operative than in America, which was much more behavioral.” Returning to New York in the early ’70s, Horowitz acted Off Broadway and in regional theaters. He had a four-day run on Broadway in Arnold Wesker’s “The Merchant,” one of the more legendary failures in the annals, before turning his energies to company-building. Horowitz’s experience in the regions became, he says, a lesson in how not to build young audiences. “In regional and touring companies, I saw that the material presented to young people was usually watered down,” he says. “I felt serious work should be seen by students as well as adults. We began as a touring company. The original name was going to be For a National Theater Seeking More Audiences — Fantasma. I got talked out of it.” After four years on the road, Horowitz got a commission from the New York City board of education to produce “A Midsummer Night’s Dream.” His notion was that to be meaningful, theater for students needs to be presented in a theater. He convinced the late Joseph Papp to give him the New York Shakespeare Festival’s Anspacher Theater for those performances. With Papp’s imprimatur, the company finally established a real presence, and funding started coming in. Since then, Theater for a New Audience has had many homes and is now a regular at St. Clement’s. Horowitz has kept to his goal of presenting the same show to student audiences as he does to adults. Indeed, that Tuesday evening performance of “Titus” was the company’s second of the day; it was performed at 11 a.m. for high school students (must have been quite a lunch period). Currently Theater for a New Audience splits the $ 600,000 cost of the student performances with the board of education. That includes extensive in-school workshops and follow-up. “Kids respond to the same things as adults, except they’re more vocal,” he says. “They’re much more open, or innocent.” Horowitz’s goal is to build a larger and better-paid roster, and to have some money for R&D not related to production. He’s also determined to stay small, though last week a lot of producers were making their way to St. Clement’s to see if “Titus” could be moved to a larger Off Broadway venue. Despite being a minor hit, the show could only extend four performances because St. Clement’s had another tenant arriving. With an infinitesimal subscriber base — 200, count ‘em — those evening-performance seats are being filled at St. Clement’s by the kind of serious theatergoers long since regarded a disappearing breed. Tickets top out at $ 30 for a “new” audience that represents the best hope of live theater.