SAN FRANCISCO — Ringo Starr had a smart idea when he started his All-Starr Band in the late ’80s. Rather than solely covering the songs his former bandmates sang in the ’60s and ’70s, he surrounded himself with talented musicians who had their own success, letting his band change gears as frequently as the lineup morphed. There have been about 50 members over the years, not including guests like Bruce Springsteen, which brings the number closer to 100. This has let Starr explore the discographies of Joe Walsh, Dr. John, The Who and many more.

The current lineup is as eclectic as ever, and at the first of two Bay Area shows this week, Ringo and his all-stars covered the songbooks of Toto, Edgar Winter, Men at Work and Average White Band in addition to Starr’s solo catalog and a handful of Beatles classics that repeatedly brought the mostly older crowd to its feet.

“I’ve played San Francisco many times but I’ve never played this place!” Ringo said after the first couple of songs, an uproarious cover of Carl Perkins’ “Matchbox” and solo song “It Don’t Come Easy.” Throughout these first couple of songs he swayed left to right at the front of the stage, microphone in hand, while all-star session musician Gregg Bissonette handled the drumming.

It was “Ringo Starr” on the bill, yet Toto guitar shredder Steve Lukather and saxophonist (multi-instrumentalist, really) Warren Ham shared many of the starring solos, both on the Toto songs and those of the other musicians.

Lukather was everywhere, soloing on the twangy Beatles tune “What Goes On,” climbing higher and higher up his fretboard on extended jams at the end of “Rosanna” and “Africa,” laying down the heart of “Hold the Line,” and blues licks on a cover of The Isley Brothers’ “Work to Do.”

When Ham wasn’t duetting with Winter on a sax, he was adding iconic harmonica blasts on “What Goes On” (which Ringo Starr pointed out is the only Lennon-McCartney-Starkey composition) and “Rosanna,” the flute lines on Men at Work’s “Down Under” and others, and some hand percussion.

Not to be outdone was Edgar Winter, who’s most famous for “Free Ride” but had numerous tricks up his sleeve, switching off between his keyboard station, a saxophone and his over-the-neck keyboard (not a keytar).

He laid down choice lines on “Free Ride,” leading the charge on a gruff and rollicking cover of Chuck Berry classic “Johnny B. Goode,” and showing off his keyboard skills on “Frankenstein,” during which he soloed for a good few minutes. Even Lukather took a short break to watch (before taking over again, of course). Winter’s voice was like sugar crystals going down your throat; rough but sweet. He even did some skating on this song. And whenever he spoke, Winter was also the comedic relief, finding nonsensical alliterative phrases to introduce bandmates and show praise.

Hamish Stuart of Average White Band and Colin Hay of Men at Work provided the evening’s foundation, with Stuart on bass most of the night and Hay laying down bluesy guitar lines. Both sang harmony on other artists’ songs but shined on their own.

On Men At Work’s “Overkill,” Hay’s vocals sounded as strong as they do on the record. Stuart was clearly having fun on Average White Band’s “Pick Up the Pieces,” a mostly instrumental classic with Ham and Winter both on sax. Stuart also dedicated “Cut the Cake” to Tower of Power drummer David Garibaldi, who watched on from the back of the floor.

As for Ringo Starr himself, he was a host and ringleader as much as a band member. Starr told short stories between songs, sang lead on some songs, and more often than not sat and drummed along at his kit at center stage, alongside Gregg Bissonette. He was clearly playing, but Bissonette was charged with the trickier and faster fills and parts. Most of those in the room appeared to be glad to share a space with the Beatle, nor did they demand more than what the Starr, now 82, was prepared to give.

“This song was written for me by my good friend John,” he said by way of introduction for his solo song “I’m the Greatest,” before teasing a couple of other covers with Lukather and then getting into “Yellow Submarine.”

Ringo took a two-song break off-stage midway through the show, which allowed Winter to go off on a nearly seven-minute rendition of Frankenstein that included a snippet of “Come Together” and a couple of others songs.

When Starr returned, he went from “Yellow Submarine” to the happy-go-lucky Beatles tune “Octopus’s Garden.” The melodic song featured Ringo’s strongest vocals of the night. He and the band followed that up with solo song, “Back Off Boogaloo,” the heaviest song of the evening, ending on a snippet of “Helter Skelter.”

Another highlight was a cover of the Beatles’ “I Wanna Be Your Man,” from their 1963 sophomore album.

The band brought things home with, “With a Little Help From My Friends.”

Follow editor Roman Gokhman at Twitter.com/RomiTheWriter. Follow photographer Gary Chancer at Instagram.com/Garych007.