Kickstarting a successful rebranding of Universal’s near-$1 billion Jason Bourne franchise, “The Bourne Legacy” scored an estimated $40.3 million in its domestic debut, plus $7.8 million from 13 smaller day-and-date territories, pointing to a muscular global run as the summer actioner expands internationally into the fall.

“Bourne Legacy,” which cost $125 million to produce, led a solid weekend of newcomers, including Warner Bros.’ Will Ferrell-Zach Galifianakis laffer “The Campaign,” which landed at the high end of expectations with $27.4 million. Sony’s adult femme-skewing “Hope Springs,” starring Meryl Streep and Tommy Lee Jones, earned $15.6 million in three days and $20.1 million in five.

But weekend totals still trailed this time last year by approximately 6%, and studios estimated that Sunday B.O. would be down significantly from Friday because of the Olympics’ Closing Ceremonies.

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As the first “Bourne” film to topline Jeremy Renner instead of Matt Damon, “Bourne Legacy” marks the latest Hollywood effort to reboot a franchise when a straight-up sequel wasn’t possible.

The result: Filmgoers continue to embrace the familiar — even with a substantially altered DNA — when it comes to summer tentpoles.

Warner’s “The Dark Knight Rises” fell behind “Bourne” and “Campaign” with an estimated $19.5 million. The blockbuster dropped 45% in its fourth frame — more than “Dark Knight,” which fell 39% during its comparable outing. But “Dark Knight Rises,” at $390 million domestically, should surpassing “The Hunger Games,” with its $407 million cume, to become 2012’s second-highest grosser Stateside.

Specialty titles hit their own benchmarks this weekend, including Fox Searchlight’s romantic comedy “Ruby Sparks,” which crossed $1 million in its third frame, and Sony Pictures Classics’ “To Rome With Love,” which reached $15 million after eight weeks.

Arc Entertainment’s 3D action comedy “Nitro Circus the Movie,” meanwhile, grossed $1.2 million from 800 playdates. Pic opened Wednesday and has cumed $2.2 million.

In far more limited release, Magnolia’s “2 Days in New York,” co-written and directed by Julie Delpy, who stars alongside Chris Rock, averaged a decent $13,500 from two debut engagements; it has been available on VOD for about a month. Spike Lee’s “Red Hook Summer,” from Variance Films, opened at four locations and averaged $10,525.

B.O. ‘Bourne’ again

Universal had hoped its fourth installment of the “Bourne” franchise would work without Damon; other studios have had success with previous reboots like “Casino Royale” and “Batman Begins,” and this summer, Sony took a similar approach with the reboot of “The Amazing Spider-Man,” which has cumed $691 million worldwide.

That sort of benchmark won’t be possible for “Bourne Legacy,” as 2007’s “The Bourne Ultimatum” is the franchise’s highest-grossing installment with almost $443 million globally. But U should be happy with the fourth outing, which will most likely become profitable and appears to have breathed new life into the series.

“This successful opening gives us freedom to take the franchise in a number of different directions,” said U distribution prexy Nikki Rocco.

Judging by how its three predecessors fared domestically, “Bourne Legacy” could cume at around $150 million Stateside — a 3½ to four times multiple based on its opening. Pic should play well throughout the summer given its fine B CinemaScore rating, but it’ll have some competish next weekend from “The Expendables 2.”

International prospects for “Bourne” are more difficult to predict. The franchise’s overseas popularity has grown steadily since 2002: “Ultimatum” nearly doubled the overseas tally of “The Bourne Supremacy” in 2004. But the absence of Damon could have a larger impact among overseas auds: outside of “The Avengers” and “Mission: Impossible — Ghost Protocol,” Renner hasn’t had much international exposure.

Still, “Bourne Legacy” marks a franchise-best opening in all 13 territories where it opened this weekend throughout Asia and Eastern Europe.

Warners, which launched “The Campaign” in Australia to an estimated $2.1 million, reported that, like “Bourne,” the R-rated laffer earned most of its domestic opening from men over 25. “The strength of ‘The Campaign’ is coming out of the Midwest and the South,” noted Warner domestic distribution chief Dan Fellman, who added that the film’s less-than-desireable B- CinemaScore is akin to what some of Ferrell’s highest-grossing pics have earned.

‘Hope’ springs for Sony

The Culver City studio is positioned nicely with “Hope Springs,” as it jointly acquired the film with MGM for a deal in the mid-teens. Sony has seen notable success during this timeframe with such past female-skewing hits as “Julie and Julia” and “Eat Pray Love.” “Springs,” which received a B CinemaScore, could play comparably to those films if word of mouth stays strong.

“I certainly expect the multiple to be upwards of five times (the film’s opening),” said Sony distrib topper Rory Bruer. “This is going to work out very well for us, there’s no doubt about it.”