When Joe Russo dove into the deep well of Grateful Dead music with alumni Bob Weir and Phil Lesh in their offshoot group Furthur, the drummer never figured that he’d launch his own band to tap the same reservoir.

He describes Joe Russo’s Almost Dead as a “lucky goof,” an idea to fill the second night of a 2013 Brooklyn Bowl party that began with his Led Zeppelin cover outfit Bustle in Your Hedgerow. Yet the quintet soon transcended other bands that interpret the Grateful Dead songbook, pushing the parameters of those venerated tunes with fiercely creative improvising.

“We’re constantly in awe of what it’s become,” Russo says of JRAD, which returns to House of Blues on Dec. 8 and 9. “It was exciting to spend all that time learning the language of the Grateful Dead and then speaking it with my friends.”

Indeed, it’s about the peer relationships that Russo, 40, forged for decades. He met keyboardist Marco Benevento during middle school in New Jersey. Bassist Dave Dreiwitz (of the band Ween) and guitarist/singer Scott Metzger, both from Jersey, guested with the Benevento/Russo Duo (which also briefly merged into a quartet with Phish’s Trey Anastasio and Mike Gordon in 2006). Only Philly guitarist/singer Tom Hamilton, whose band American Babies once included Russo, came into JRAD with an early indoctrination to the Dead.

Russo instead grew up as a metal-head who worshipped Black Sabbath and Iron Maiden. “I talked mad shit about the Grateful Dead when I was a kid,” he says. “I got to high school and [students] were all wearing tie-dye and I was still wearing my black T-shirt. It took me a lot longer to get there.”

Now he’s glad for the evolution, while suggesting that if he heard adventurous Dead fare like “King Solomon’s Marbles” from 1975’s Blues for Allah in his teens, he might have been hooked then. Russo particularly favors the early Dead from the late ’60s for its raw, aggressive attack. “There’s a punk element to it,” he says. “Nothing was really pensive. It struck me as so uncalculated.”

In turn, JRAD bucks expectations beyond stretching traditional Dead epics like “Terrapin Station” or “The Other One.” A straightforward tune like “Althea” or “Throwing Stones” can also divert into a jam that highlights a set.

“There’s no programming in the sense that ‘This is a first-set song’ or ‘This song goes like this,’ ” Russo says. “We’re not tethered to these ideals that everybody else playing this music seems to be tethered to.”

The same goes for genre-crossing teases as well as tunes close to the Dead sphere, like those of Bob Dylan or the Band. “We’re a bit tease-heavy as a band,” Russo says, noting that they try to amuse both fans and themselves. “Somebody will play something and all of a sudden we’re playing a Lorde song. Again, we don’t paint ourselves into a corner where we’re not allowed to do something. … Those are the true moments, where you’re having a conversation with a friend.”

One week after the JRAD shows, Russo will return to town with newer friends for Alone & Together. That Dec. 16 concert at Royale features singer/songwriters Elvis Perkins, Eric D. Johnson (of Fruit Bats), Josh Kaufman and Sam Cohen, who shares a studio with Russo and once co-fronted Boston’s Apollo Sunshine.

It’s essentially a song swap where they sing one another’s music. “This one just clicked because of the personalities,” Russo says of the recurring series that hit Newport Folk this year, with Kevin Morby in Perkins’ spot. “I’m kind of getting to be a fan while being onstage with these guys, just playing a supportive role.”

Russo writes as well, but don’t expect to hear his tunes at House of Blues. “While we take the improv route, writing music for [JRAD] at this point seems odd,” he says. “People want to hear these amazing songs by the Grateful Dead or [in that] canon, and they want to hear us play the cracks in between.”

His old Furthur bosses are cool about JRAD too, says Russo, who just saw Weir fronting Dead and Company. “Bob busts our balls for playing too fast.” ◆

Joe Russo’s Almost Dead plays House of Blues on Dec. 8 and 9.

For more music coverage, check out Paul’s Weekend Music Ideas at improper.com.