I just used MVC and Marvel/Dc as examples. To show how multiuniverse games aren't inherent failures. As far as story line goes that is relative to how good the writer is not the idea.
I will write up a starting scenario for giggles to give an example of how the beginning of a new game could potentially be represented.
Scenario: You chose RedXIII's (Nanaki's) Race and so you are starting in Cosmo Canyon. (note: warrior is not indicative of the warrior class job but a title dont get that confused.)
You are awoken by the sound of a tap on your door; as you wipe the sleepiness from your eyes you see a man materialize before you. He tells you that today is the full moon and you must go through with your tribal rights to become an adult and to be recognized as a warrior. This is something that all warriors must do.
You follow the man to the top of Cosmo Canyon; as you enter you meet with Nanaki who describes the arduous task that awaits you. (You later find out that Bugenhagen as since passed and Nanaki has become a leader of cosmo canyon) Nanaki tells you that you must go into the Cave of the Gi and retrieve a tier that falls from his fathers monument once a full moon.
As you set out and enter the Cave of Gi you will play through the familar territory and (not kill x amount of monsters) fight your way through the cave riddled with puzzles and treasure chests. You are stopped right before you exit the cave where Nananki's father resides by (the first boss fight) Gi Nattak.
After you defeat Gi Nattak you proceed through the exit and walk up to Nanaki's fathers stone arrow riddled body and wait as the moon arises. You stare into the moonlight and the silence is disturbed by soft footsteps. The alien noise that disturbed the still silence was belonged to Nanaki. Nanaki tells you of the tribes history and gives you a ceremonial pin signifying your acceptance as a warrior and adult in the tribe.
So there ya go. It represents the warrior race that is nanaki throws you directly into combat as most FF titles are known for. I am sure if you wanted to do something like that with the Ronso race you could. Point being is that you can be creative and original with pre established storyline.
If I were to tie multiple universes together I would use something that has existed in a form in all FF games, which would be Crystals that are the 4 elements. Also every FF has a political/corrupt government theme so I would also probably use those themes to centralize a universal theme and tie the story together. Just saying it could be done and done well.
Hell you could even put a CCG in the game and challenge people to games for gil etc. Something like FF8 or FF9. God why not just do that in FFXIV?
I never understood how developers dont think of the most simplistic elements that could make a game go from O.K. to amazing.