Elvis Costello can keep a high or low profile, but his fans will turn out to fill the Warner Theatre on Thursday. (Charles Sykes/Invision/Associated Press)

Elvis Costello Show: Thursday at the Warner Theatre. Show starts at 8 p.m. 202-783-4000. warnertheatredc.com. Sold out.

Elvis Costello has achieved an almost perfect level of celebrity. He’s famous enough to tour and record whenever he wants, but not so famous that he’s hounded by paparazzi. He’s famous enough that he can keep a regular band together and also collaborate with everyone from Loretta Lynn and Tony Bennett to Rhiannon Giddens and Gov’t Mule, but not so famous that he has to play stadium shows.

His regular band, originally called the Attractions and now called the Imposters, has always included keyboardist Steve Nieve and drummer Pete Thomas. (Davey Faragher has replaced Bruce Thomas on bass.) They will join him at the Warner Theatre on Thursday.

But when Costello came to the Newport Folk Festival in July, he appeared not with the Imposters, but with the female duo Larkin Poe for an off-kilter, all-acoustic treatment of “Pads, Paws and Claws.” He then joined the Preservation Hall Jazz Band for a Dixieland treatment of “Sulphur to Sugarcane,” which he introduced as a campaign song for 2016. Middle Brother, the Dawes spinoff project, backed Costello on “Everyday I Write the Book.” There was also time for a solo piano version of “A Face in the Crowd,” the title track from a stage musical he’s working on based on the Budd Schulberg story “Your Arkansas Traveler.”

Costello could never pursue all these different musical paths if he didn’t have a Goldilocks sort of fame: not too hot, not too cold, just right.