Once you pledge allegiance to one faction, your allegiance will stay for a week. I assume that Bungie meant until the weekly reset with "for a week". You cannot pledge allegiance to another faction during this week, you will have to wait.
You can only hold one at a time, its not like the faction cloaks, marks, or bonds. If you want to get dead orbit rep and you have future war cult allegiance you will have to wait a week before you can change the allegiance you will go into next. You CANNOT hold multiple allegiance s at a time.