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Call it the rule of four, or Brazil’s first studio-sized alliance.

Hollywood’s studios used to have a lock on big Brazilian movies’ distribution. In 2012, however, six of the top seven Brazilian films were co-financed and promoted by a four-way alliance: RioFilme; Globo Filmes, the film arm of broadcast giant TV Globo; Downtown Filmes, Brazil’s largest Brazilian pic distributor; and Paris Filmes, Brazil’s biggest distrib overall.

The most recent of these six films, lead-produced by Mariza Leao’s Morena Filmes, is Roberto Santucci’s sex comedy “Upside Down 2.” It opened Dec. 28 to a first-weekend take of $2.8 million, the third-biggest bow ever for a Brazilian film. By mid-January, it was tracking for a $20 million-$25 million B.O. haul.

Only one U.S. major, Warner Bros., distributed a Brazilian pic title in the top 10: Andrucha Waddington’s “Party Crashers.”

For 2013, RioFilme is also teaming with other distribs on potential blockbusters: “The Dognapper,” with Imagem, and “Faroeste caboclo,” with Europa Filmes.

Why the local distrib push-back?

Under Brazilian law, U.S. studios can invest into local films 70% of taxes on profits in Brazil. But Brazilian DVD markets have plunged. Increasingly struck in L.A., Brazilian TV deals no longer generate so many local tax credits. So studios’ tax coin has decreased.

There’s also the RioFilme factor.

“RioFilme has given us the power to battle the studios for the best projects,” says Downtown’s Bruno Wainer. “We’re a kind of local major, a powerhouse, with a long-term project for the future.”

Additionally, Brazil’s economy decelerated in 2012, growing less than 1%.

But Brazil is one thing, its film economy another, argues RioFilme CEO Sergio Sa Leitao. Thanks to multiplexing, Brazil’s movie market has grown seven years in a row, reaching $784 million in 2012, according to trade publication Filme B.

Still grossly underplexed, Brazil’s film biz will build for the foreseeable future: The more films RioFilme or Rio companies back, the bigger their share of an ever-larger B.O. cake.

RioFilme can move decisively, investing about 20% of films’ budgets — about $490,000- $735,000 per participation — and 20%-40% of P&A coin in distribution, per RioFilme COO Adrien Muselet.

Says Sa Leitao: “A RioFilme investment in production or distribution reduces risk and maximizes gain for all parties involved. It helps attract other investors, minimize production length and avoid launch delays.”

Moving fast, RioFilme and producers can often beat studios to big projects. Partners welcome its rapid reflexes.

“Considering the bureaucracy in Brazil, speed marks RioFilme productions,” says Leao.

“Upside Down 2,” for instance, was green-lit in late 2011 and released in late 2012.

RioFilme “now represents a classic example of ‘de-bureaucratization,’ a modern management and very little red tape, standing in stark contrast to the federal government’s habitual bureaucratic procedures,” adds producer Luiz Carlos Barreto.

RioFilme has also sagely zeroed in on a rich vein of contempo comedies that capture a national zeitgeist, a society’s strains as it hurtles towards modernity.

Roberto Santucci’s “Till Luck Do Us Part” depicts a family nearly torn apart by its rabid consumerism after winning the lottery. Felipe Joffily’s “Did You. . .Score?” and “Party Crashers” plumb men’s insecurities hidden behind macho facades.

Turning on a workaholic sex-shop-chain owner, the “Upside Down” franchise “portrays 21st-century women, their difficulties balancing work and private pleasure,” Leao says.

“Brazil’s social landscape is evolving really fast. People have far more freedom, ways to make a living. It’s great raw material for comedy,” Muselet says. “Many of them are about how people try to get a better life, even having to work 12 hours a day to do so.”

Rio movies’ share of Brazilian films’ B.O. soared from 69% in 2008 to 95% last year, Sa Leitao says.

But challenges remain, he maintains. Thirty-three studio-distribbed U.S. movies still made Brazil’s box office top 50 last year.

Beyond comedies, biopics and thrillers, “We have to become increasingly competitive no matter which kind of films we do, including art films,” Sa Leitao says.

RioFilme put up $500,000 to entice “The Twilight Saga: Breaking Dawn — Part 1” to shoot in Rio.

The city now needs a regular international shoot rebate system, Sa Leitao argues: “Brazil is the last country with a major local film industry but no incentives to attract international film productions. We must change that.”

RioFilme @ 20
RioFilme fuels Brazilian biz | Big players take control of market | Ups and downs of building biz | Duo helps industry develop | RioFilme’s slate