I would actually like if the greater evil they mention that Cole is being prepared for is something other worldly.  Kind of like Apocalypse or Galactus, something where everyone has to come together to defeat it, and Cole has been prepared by his future self to lead the rebellion instead of run away and hide like future Cole did.  Not sure if that would make the better game, but it would make a more fun story for me.

Maybe both? The government trying to gain more power+ repel threats, and outer unknown force?

That could work, kinda like the government is Shield and they try to use the Ray Sphere to make more heroes, and Cole has to fight on both sides to keep innocents from dying and fight off the greater threat.  I like it.

EDIT: Post contains SPOILERS!!

I figured we'd be seeing something about "the beast" mentioned at the end of the game after you beat Kessler. Since that's why he went back and did all this stuff to Cole, it made sense to me...

I suppose they could have something else going on with "the beast" being the "behind the scenes" mastermind behind everything.

Maybe they can make it Deus Ex-ish and have 3-4 factions. Maybe John can become a superhuman who wants to prevent the government (which he feels is compromised) from getting the ray sphere. Some outer force that believes humans shouldn't have such powers because of their hatred and selfishness (which Cole can disprove), a rogue agency/terrorist group that are similar to the "Voice of Survival", and the government who both want to repel this threat, but also use it to gain immense power.

And maybe we can add the illuminati?