George Lucas has made a whole career out of the idea.
On TV "Lewis" is as good as "Morse" ever was even though lacking the one magic ingredient of John Thaw.
Z Cars spawned a number of spin offs, which were very good, called "Softly Softly" and then "Barlow" and for those old enough the remember "Murder Bag" with Det Insp Lockhart which became "Crime Sheet" and then with a "promotion" to Det Superintendent Lockhart the series became "No Hiding Place" and ran for many years producing a couple of admittedly not very successful spin offs of its own. Lockhart was played for years by actor Raymond Francis and if memory serves at least one of his "Sidekicks" a Detective Sergeant Baxter (played by Eric Lander) starred in his own show called "Echo Four Two", another police drama for a while before being replaced by actor Johnny Briggs later to become famous as spiv "Mike Baldwin" in Coronation Street.
So yes sometimes spin offs can work but often they need the same actors to pull it off as with the TV series quoted above .... at least some of the actors carried on, all be it with a "promotion" so the thing became believable. Whether a prequel to Fools & Horses will work is questionable. I would like to have seen David Jason playing his own father ... that could have worked.
