Just Google “Rat Pack revue” and you’ll get plenty of results; every two-bit talent booker in the country seems to have a stable full of Franks and Deanos and Sammys.

“Sandy Hackett’s Rat Pack Show,” coming to the 4th Street Theatre next week, is different for two reasons. First: It is not just a revue; it’s a musical with a narrative. Second: Its star actually grew up around Frank Sinatra, Dean Martin, Sammy Davis Jr. and Joey Bishop. Hackett is the son of comedian Buddy Hackett, who was close with Bishop and ran in the same Vegas and Hollywood circles as the other three.

What that means in terms of the product on stage is difficult to say. But, if you were the sort of person inclined to buy a ticket to a show full of entertainers pretending to be other entertainers, wouldn’t you want the one who had a guy who actually knew those other guys?

Hackett, whose father, Buddy, died in 2003, knew Bishop well enough to call him Uncle Joey. When HBO made “The Rat Pack,” a 1998 TV movie, Bishop called the younger Hackett, at the time a bit-part actor who had studied hotel management in college, and told him he’d be perfect to play Bishop in the film. One problem: Bishop wasn’t actually involved in the production and had no say in the casting. Still, that planted the idea in Hackett’s mind of creating a show in which he could play Bishop.

“They didn’t want me,” he says of HBO. “But Joey wanted me. That sent me in this direction.”

Hackett had worked with Bishop years earlier on a failed TV pilot, so he had gotten to know Bishop professionally as well as personally. He saw the work ethic and the talent that had made the Rat Pack such a big draw back in the 1960s.

In those days, if Sinatra was playing a gig at a Vegas casino, it wasn’t at all uncommon for Martin, Davis or Bishop — or all of them — to join him, even if they weren’t originally signed up for the show. Audiences loved it.

“They were huge shows,” Hackett says. “And instead of just getting one of them on stage, you got all four. It became a big event.”

The interplay of the four, which came off as loose and drunken, was actually studied and professional. They were old-showbiz guys, and putting on a show meant Putting On A Show. That’s the sort of feeling that Hackett believes he’s captured with this stage production, which debuted in 2002.

The show has gone through several cast changes since its first run. The current edition of “Sandy Hackett’s Rat Pack” features Danny Grewen as Sinatra, Louie Velez as Davis, Tom Wallek as Martin and, of course, Hackett as Bishop. But it’s not just a re-enactment of one of those ’60s shows. It’s a narrative about God sending the Rat Pack back to Earth in modern times to put on a show. It features Hackett’s famous father, in a voice-over recorded before his death, as God. It also features Hackett’s wife, singer Lisa Dawn Miller, whose father, Ron Miller, wrote a string of hits such as “For Once in My Life.”

“I didn’t want a cheesy tribute show,” Hackett says. “I wanted a theatrical production. ... God sends them down to do one more show, because they’re causing too much ruckus up in heaven.”

That said, Hackett’s show doesn’t reinvent these characters. That’s not the idea. They remain as popular as they are because each was an indelible character already. So what he did is create a narrative device that can best display those talents, as well as the relationships they shared with each other.

“This show is about relationship, relationship, relationship,” Hackett says. “Nothing has changed. I don’t try to rewrite the essence of what they did.”

There is some improvisation in the humorous parts of the show, but that too is in keeping with the original Rat Pack style. Hackett reads the local papers when he’s on tour so he can do topical material as Bishop would have. That’s good for the audience, but it’s also good for the players, in that it keeps the show fresh for them as well, he says.

“I love ad-libbing,” he says. “It’s what I grew up doing. I’m not going to just get up there and do my act.”

The effect, Hackett says, is not unlike the effect of a show with Frank, Deano, Sammy and Bishop.

“People say to us after the fact, ‘It’s everything we expected and yet so much more,’” he says. “The show delivers. We’ll make you laugh. We’ll make you cry.”