Not many bands can stretch two dozen songs over a three- to four-hour set while veering from jazzy to groovy to country to psychedelic. Matter of fact, not many bands can even play that long, would want to or draw fans who would hang through it.

That’s just part of what makes Phish such an odd duck in the pop/rock landscape. Add to that that Phish, despite a nearly 30-year history, isn’t associated with any big radio jam or classic track, like its forebears, the Grateful Dead, had with “Truckin’ ” or “Touch of Grey.”

None of that has stopped Phish from being one of the few rock bands of its day that can pack a 20,000-capacity venue such as the First Niagara Pavilion.

Phish and its hard-traveling phans return there Saturday for the first time since the reunion tour in 2009. It’s the 10th show and sixth city on a summer tour that started with a two-night stand in Worcester, Mass., earlier this month.

True to form, the tour is packed with “event” shows. On June 10, it returned to Bonnaroo in Tennessee for only the second time, playing a rainy-night set that will be remembered for country (and psych-rock) legend Kenny Rogers joining them for “The Gambler.” The cameo drew mixed reviews from Phish phans, who were divided about the whole show in general. “I don’t even count it as a Phish show,” one phan posted, arguing that it was more geared toward the general Bonnaroo crowd than the hard-core following.

At Bonnaroo, Phish, one of the Great American Cover Bands (like the Dead), also took on TV on the Radio’s “Golden Age” and the Velvet Underground’s “Rock and Roll.” (Among the other songs covered on this tour have been Stevie Wonder’s “Boogie on Reggae Woman,” Bob Dylan’s “Quinn the Eskimo,” Ween’s “Roses Are Free,” the Beatles’ “A Day in the Life” and Talking Heads’ “Crosseyed and Painless.”) Billboard listed it as one of the festival’s 10 best performances.

While June 23’s is the first Phish show here in three years, frontman Trey Anastasio — ranked 73rd in Rolling Stone’s “100 Greatest Guitarists of All Time” — has visited the local Phish community two straight Februarys with a 2011 half-acoustic/half-electric show at Stage AE and a gig this year with the Pittsburgh Symphony that demonstrated how symphonic rock should really be done.

For that show, he and his large “band” worked from a score with scant room for improvisation. Normally, Phish makes it an art, and a science, starting with its methodical approach to rehearsal.

“We’re the most analytical band, in some ways,” Anastasio told The Believer last year. “We’d talk and talk for hours about this stuff. I see improvisation as a craft and as an art. The craft part is important.”

The ever-changing set list, he said, flows out of that improvisation, making every Phish show a fresh adventure.

“Since Phish came back,” he said in that interview, “I’ll just walk around backstage and ask everybody, ‘What do you want to play?’ and people will say, ‘Oh, I want to sing this or that,’ until I have 30 or 40 songs on a piece of paper. It’s like the writing. The set lists are all over the place. Then we go out onstage and just forget about it. We give a set list to Chris every night and he just laughs and rips it up.”

Phish will perform at 7:30 p.m. June 23 at First Niagara Pavilion, Burgettstown. Visit www.livenation.com