I don't think anyone mentioned this one: Police Story. That was an anthology series in the '70s and '80s about the LAPD. Each week was a different story about different characters all from the same large agency. Sometimes it was about Patrol Officers, others it was about Detectives, and occasionally it was about those assigned to the Administration. It dealt a lot with their personal lives probably more so than their professional ones. On occasion, they brought back characters and it had three offshoots. I can see this type off premise for a Star Trek series. As others have stated, stories could take place on various ships, planets, space stations, etc. - both Starfleet and alien. Another advantage a Star Trek anthology has is so many eras have been written about that the writers could use virtually any time period as a backdrop. We could see known, established characters as cadets, teens, or even children. We could see scenes from various wars or incursions, discoveries of planets, first contacts with various races, or just a "lower decks" tale about what goes on throughout the ship day to day. It could be exciting, romantic, depressing, funny, frustrating, etc. It opens up all kinds of doors and, if done right, A-list actors may campaign to be on the show, which would bode well during the sweeps.