Okay, so I'm gonna make this short.
I picked up all the dailies in the Argent Tournament, but didn't finish them, the one that changes everyday (There are 3 possible) included.
The next day I went to pick up the rest of the dailies and I was able to pickup the "1 of 3" daily as well, so I had that daily from yesterday and the version from today as well. Maybe the screenshot will help explain this.
Tl;dr if you pick up one of the argent tournament dailies that change everyday the next day you can pick up the other one and have two at a time.