Hypothetical scenario: Dirge of Cerberus improved version
Vincent discovers (via the Turks) that one of Hojo's very early "experiments" in implanting materia escaped and is believed to be living on a hitherto unexplored part of the planet (it's not hard to add to a map, and the reason the area is unexplored is because the terrain is extremely hostile). Vincent believes this "person" may hold the secret to freeing himself of his demons, so he and Avalanche set out to find he/she/it. In order to track it down, they need Lucretia's help, so they wake her from her sleep and (reluctantly on the part of some members of Avalanche) take her with them. They also have to gather various clues and background information which are scattered around the Planet, necessitating a visit to all our favourite old haunts, including Nibelheim. I guess crystals would have to be involved in some way. Maybe as drugs?
Rufus Shinra is also after the escaped experiment, since he believes it may contain patented Shinra secrets which will be valuable to him in the new pharmaceutical industry he is setting up. Thus the Turks and Avalanche are once again pitted against each other. You have the option to play as either party, by which I mean there would be essentially two narrative arcs - so you can play once as Avalanche and then again as The Turks and you would get a different story, different adventures, different bosses in each story. Eventually, however, they have to combine their efforts to defeat some as yet undefined Boss which has nothing to do with Jenova, Sephiroth, Genesis or Minerva.
It would not be a first person shooter.