Gary Sinise, left, and Daniel Henney in "Criminal Minds: Beyond...

Gary Sinise, left, and Daniel Henney in "Criminal Minds: Beyond Borders." Credit: CBS / Darren Michaels

The minds of criminals aren’t limited to one country . . . or to one show.

CBS’ long-running “Criminal Minds’’ attempted a spinoff series in 2011 — the short-lived, Forest Whitaker-starring “Criminal Minds: Suspect Behavior’’ — and the show’s makers are ready to try again. Premiering right after the original drama Wednesday (with Joe Mantegna making a crossover appearance), “Criminal Minds: Beyond Borders’’ returns “CSI: NY’’ alum Gary Sinise to the network and the role he originated in a “Minds’’ episode last season: Jack Garrett, leader of an FBI International Response Team dedicated to helping Americans who run into danger overseas.

Alana De La Garza (“Law & Order,’’ “Forever’’) also stars as a former agent who left for reasons both personal and professional but agrees in the premiere to help Jack find several volunteer workers who vanished in Thailand. Daniel Henney (“Revolution”), Tyler James Williams (“Everybody Hates Chris,” “The Walking Dead’’) and Annie Funke (“The Affair’’) play the other members of the squad, each with specialized abilities.

Executive producer Erica Messer oversees the parent “Criminal Minds’’ as well. She says she saw room to expand, though “we didn’t want to tell more stories domestically, because we feel that ‘Criminal Minds’ handles that very well, and has done so for 11 years.

“But there’s a great big world out there where Americans are traveling more than ever before, and when we did the research and found that 68 million Americans leave the United States every year, our brains just started ticking that there’s crime that happens to those Americans. And wouldn’t it be amazing if there was a team of FBI heroes that could come save you?’’

As the chief of those heroes, Sinise is looking beyond the case of the week, conceding there are similarities between his new character and Mac Taylor from “CSI: NY.” “You always see these characters that are constantly broken,’’ the Emmy-winning actor reasons. “They’re dealing with a lot because they deal with such a dark world. There’s always multiple divorces, and they’re going through a lot of pain in their own personal lives.

“On the other hand, there are law-enforcement individuals in this country that have found a way to have a successful family, to raise kids, to keep their marriages together . . . all of that. I know several of those people personally, so we decided to do that with this character, to show somebody who was able to balance home and work, even though he’s dealing with a pretty dark world that these individuals go into constantly.’’

Though much of “Beyond Borders’’ ostensibly unfolds on foreign turf, locations close to the series’ Southern California home base stand in for other lands. “I’m constantly amazed by their interpretation of each country,” De La Garza says of the show’s production-design and set-decoration team. “I traveled a lot when I was younger — not that I’m not young! — and I’m in awe of their talent. When we’re supposed to be in India, it looks just like India. They’re incredible.’’

Projecting why “Beyond Borders” may work where “Suspect Behavior’’ didn’t, executive producer Mark Gordon (whose current shows also include “Grey’s Anatomy,’’ “Quantico’’ and “Ray Donovan’’) says: “It’s always tricky when you have a show that is franchisable. ‘Criminal Minds’ was that show, and we were obviously very excited about the idea when we created ‘Suspect Behavior’ to take advantage of it. Whether you’re a new show or whether you’re a spinoff, it doesn’t always work. I think that, quite honestly, one of the things that did not help us with the audience with ‘Suspect Behavior’ was that we were trying too hard to be different.

“When you are creating a spinoff, you want something that’s fresh and different,’’ adds Gordon, “but at the same time, you want to honor the show that you’re spinning off from. And I think that sometimes the desire to, frankly, have an opportunity to create more is not always the best way to create a great show. [This was] taking the right opportunity to create the right show that was organic and would be correctly in the ‘Criminal Minds’ family but had its own identity. Erica came up with this idea, and it felt like we have it. And here we are.’’

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