It’s not uncommon for a TV series to be created as vehicle for a single person who both stars in and writes the show. An example of this is Seinfeld, whose star Jerry Seinfeld co-wrote most episodes of the first two seasons (with sporadic writing credits thereafter).
What is much less common is for multiple regular cast members of a TV series to also serve as regular writers of the show. Where this does occur, it tends to be writing partners (Fawlty Towers, written by and starring John Cleese and Connie Booth) or established double acts (Bottom, written by and starring Rik Mayall and Adrian Edmondson). If more than three actor–writers are involved, it tends to be with sketch comedies like Monty Python’s Flying Circus, where all episodes were co-written by all six regular cast members, and Saturday Night Live, where in any given season several of the cast are usually also on the writing staff.
Are there any shows other than sketch comedies where three or more regular cast members are also regular writers?
The only one I can think of is the American version of The Office, where regular cast members B. J. Novak, Mindy Kaling, and Paul Lieberstein wrote about a quarter of the show’s 200 or so episodes, usually independently rather than jointly. (Steve Carrel also wrote two episodes, but this isn’t enough to count him as a “regular” writer. In a similar vein, Michael Schur wrote and appeared in about a dozen episodes, but he was never billed as a regular cast member.)
Gina Yashere played a regular character in the first 4 seasons of Bob Loves Abishola (and a recurring character in the last season) - and she is created as co-writer of the script or story for many episodes.
The TV Land sitcom Teachers was created by a comedy troupe called The Katydids. IMDb shows at least 10 “written by” credits for 5 of the main cast.
Likewise, the truTV sitcom Those Who Can’t was created by a comedy troupe called The Grawlix. IMDb shows at least 7 “written by” credits for 3 of the main cast.
The show Workaholics was created by a comedy troupe as well. IMDb shows at least 7 “written by” credits for 3 of the main cast.