There were some efforts to have Data in charge of another shift (when they pointlessly turned down the lights). But in "Disaster" there was a watch officer who was killed in action (can't remember her name though), which led to Troi taking command.
In my fanfic, I like to have the other two shifts having their own Watch Officer, who is in charge of the standard day-to-day running of the ship. But when an emergency situation arises its all hands of deck and the senior staff assume their posts.
But thats just me.