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.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)