I could see this as a possibility in a Dominion-dominated alternate timeline in which the Romulans never entered the war on the side of the Federation. It's 2375 and the Merchant Marines are almost the only real contact the Federation's member-worlds have with one another as Starfleet itself falls-back and builds to a resistance strike.
The Vorta & Founders are reluctant to wholesale destroy the Merchant Marines as they're in a "war on terror" battle to win the Alpha Quadrant peoples' hearts and minds while fighting the Borg on one side and The A.Q. Alliance on the other.
The Merchant Marine vessel, XXXXXX, finds itself in Dominion territory and aiding/abetting Starfleet on-the-downlow, but otherwise finding itself in situations not unlike the Enterprise-D in the meantime.
Mostly civilians in charge with one or two formerly Starfleet officers, either disgraced or disabled or considered too old to be effective on "the line".
There's a Founder on the bridge as one of the 99 launched like Odo into space, learning about the different perspectives on the conflicts it witnesses. It was enclosed in a bundle of goods brought aboard by refugees. Believed to be an ancient relic, it was born, escaped and slithered around the hold scared shitless of everything around it.
There would be the obligatory Karemma, Yrridian, or Jem Hadar character involved at the ship's main or secondary ports of call.