We never can say goodbye, and that is especially true when it comes to beloved TV shows. The post-finale spinoff has always been a popular way to keep a franchise going.

In recent decades, some of these spinoffs have been just as good as the original: I would lead with “Frasier,” out of “Cheers,” of course, which put Kelsey Grammer’s character front and center, making him just as iconic as Ted Danson’s Sam Malone. And “Better Call Saul,” an idea that began as a bit of a lark when “Breaking Bad” was ending. Of course, Vince Gilligan and Peter Gould wound up creating something richer — a show led by Bob Odenkirk and Rhea Seehorn that went to dramatically dense places no one could have predicted. It’s an immediate spin-off all-timer. “The Good Fight” continued the legacy of “The Good Wife,” but shifted the focus to Christine Baranski. “The Conners,” of course, is “Roseanne” minus Roseanne.

But those are spin-offs that kept a universe going by focusing on what had been supporting characters. (The less we say about “Joey,” the better.) Meanwhile what has always fascinated me is when a show ends…and then immediately continues on in a new form with the same lead characters. I was too young to really understand how “All in the Family” morphed into “Archie Bunker’s Place,” and as a kid it confused me: Wasn’t “Archie Bunker’s Place” still “All in the Family,” just with Carroll O’Connor’s starring character spending more time in a bar?

The answer is “sort of,” as Jean Stapleton continued for a bit on the new show, before Edith eventually died of a stroke. Most of the cast was new, and the ratings never reached the same height as “All in the Family,” yet “Archie Bunker’s Place” still lasted four seasons.

“The Brady Bunch” spawned several sequel series with the same cast (well, mostly; occasionally you’d get a new Jan or some other swap). Remember “The Golden Palace”? It was “The Golden Girls” immediately following “The Golden Girls,” but with less Bea Arthur and more Cheech and Cheadle. “Saved by the Bell: The College Years” took the same “Saved by the Bell” stars but shifted them out of high school and into primetime.

The idea of sequel series reaches back to the 1960s “Dragnet” revival. The Peak TV era means several shows are returning with the same leads, but sometimes in new form. And in these cases, the sequel series sometimes come several years after the original. “CSI: Vegas” brought back stars William Petersen and Jorja Fox from “CSI” — and although they’re leaving after Season 1, fellow original star Marg Helgenberger is back for Season 2. “And Just Like That …” is “Sex and the City,” sans Kim Cattrall as Samantha. “Dexter: New Blood” is “Dexter” — with some new blood. You get the drift.

The MVP of this phenomenon is Amazon’s Freevee, previously known as IMDb TV. The ad-supported streamer last year revived “Leverage,” with the same producers and much of the same cast, redubbed “Leverage: Redemption.”

But again, if we’re talking about immediate sequels with the same leads (a very narrow definition, but still surprisingly common!) now comes Freevee’s “Bosch: Legacy.” The series picks up a year after the end of “Bosch,” which ran seven seasons on Freevee’s sister, subscription-based Prime Video, starring Titus Welliver in the title role.

“We always said to Amazon, ‘When you want to end the show, please let us know so we can write to an ending,’” says executive producer Michael Connelly, the author behind the “Bosch” books that spawned the series. “So that’s what we did in the seventh season with the show at Amazon. We thought the proper ending was that Bosch walks out the door and turns in his badge, which is reflective of what happened in the books.”

But then IMDb approached Connelly and fellow EPs Eric Overmyer and Tom Bernardo about a spinoff. In Connelly’s books, Bosch eventually quits the LAPD and becomes a private eye — and that narrative development became the basis for “Bosch: Legacy.”

The big difference here was to elevate the characters of Honey “Money” Chandler (Mimi Rogers) and Maddie Bosch (Madison Lintz), and turn the show into an ensemble, rather than just a Welliver-starring vehicle.

“We obviously have the same DNA in Harry Bosch, and these characters have been seen before, so we just had a lot of good things that were inspiring us to go forward with it,” Connelly says. “The anchor is always going to be Titus, but let’s shake it up a little bit, add in two characters in a big way into the mix and go forward and not look back.”

Sometimes, it’s nice to get to spend more time with some familiar faces, even if it’s under slightly different circumstances.