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Since there are several posts suggesting it, I decided to go ahead and try it out.
When one nuke is called in, and the timer is counting down, attempting to call in another nuke, whether it's yours, a teammate's or an enemy's, it will say that a nuke is already inbound.
This includes when the countdown is stopped and the entire game is about to be blown to hell.
There you go. It is not possible normally, and no glitches to do so are known yet.