Michael J. Fox was technically a supporting actor on “Family Ties,” then later become a movie star, and then his own show, “Spin City.”
Howard Hesseman played Dr. Johnny Fever on “WKRP in Cincinnati,” then later starred in that show with the classroom, whatever the hell that was called.
Think harder. How about Gavin McLeod from the same show, who went on to star in The Love Boat?
Teri Hatcher from **Lois & Clark: The New Adventures of Superman ** to Desperate Housewives.
Head of the Class.
Melina Kanakaredes went from supporting roles on sucessful shows, such as Guiding Light and NYPD Blue, to star in her own series, Providence.
He was one I considered. But he won an emmy for Best Actor while on Family Ties, so I didn’t cite him.
Good example.
Also, I thought of a few other qualifiers: Marky Post from Night Court MAY qualify for her show Hearts Afire. She shared the lead with John Ritter and it lasted three seasons.
If we count that, then add John Larroquette. His show lasted four.
Love Boat was kitschy, but it wasn’t a sitcom. He certainly was a lead.
Paul Lynde went from occasional appearances as Uncle Arthur on Bewitched to more or less starring on Hollywood Squares, then hosting his own variety show in the early 1970s.
Do soap operas count? If so, Sarah Michelle Gellar started as a child actress in a supporting role on a soap (was it All My Children?) before becoming a huge star as the title character from Buffy the Vampire Slayer.
… and then Penny Marshall went from Happy Days to Laverne and Shirley, and then that whole directing/producing gig.
Three years in a row, no less, so I guess he’s disqualified.
Lemme see if I have the rules straight. Show A and Show B both have to be hits, both have to be comedies, and the actor in question had to have been a supporting actor in Show A before starring in Show B as a different character (no spinoffs). Right? The idea being that very few great supporting/ensemble actors can carry a show by themselves?
Sorry, I can’t think of anyone who hasn’t already been mentioned. If you allowed spinoffs, I might consider Charlotte Rae (from Diff’rent Strokes to The Fatcs of Life), Jim Nabors (from The Andy Griffith Show to Gomer Pyle), or Penny Marshall and Cindy Williams (from Happy Days to Laverne & Shirley), but I’m not even sure those are exactly what you’re looking for.
I’ll admit there are a lot of rules.
You summarize them accurately. 
What about Bill Cosby? From “I Spy” to “The Cosby Show.”
I dunno about the Doogie thing - he wasn’t a side character in Doogie MD …
But in that same vein, I’d add Cybil Shepard from Moonlighting to Cybil (well, I loved it).
I don’t understand why the side kick girl from Dharma and Greg didn’t get her own show - (and the Scientology wierdo did, turned inside out and backwards).
I wonder if Mork and Mindy counts? Mork went from Happy Days to Mork and Mindy, (guess that is a spinoff) and Mindy went to My Sister Sam until she was killed off.
Then there’s Sports Night and Six Feet Under 
which also spawns Sports Night and Desperate Housewives with “Dana” and “Susan” becoming and “lynette” and “Mary Alice”
Nice one!
Didn’t one of Carla’s husbands (of Cheers) do their own show, too?
Meredith Baxter-Berney was on Petticoat Junction, then Bridget Loves Bernie as a star (which was a hit show, though only lasted one season), then was supposed to be the star of Family Ties.
Dear John - wasn’t Judd on Taxi, too? DJ ran a long time, I thought.
Jerry Seinfeld was a regular in Benson for a season.
Richard Mulligan went from part of the cast of Soap to the lead in Empty Nest.
Conrad Bain was a supporting character on Maude and to top billing on Diff’rent Strokes.
George Clooney went from “E/R” to “Facts of Life” to “Roseanne” before breaking out in “ER.”
And don’t forget she was Myrna Turner on *The Odd Couple * before that.