This is a bit of a juvenile scenario, but this has been on my mind.
Let's say Ahab heard from another whaling ship that some unknown sea creature had killed Moby-Dick. Or perhaps the crew of the Pequod arrives just in time to witness another giant beast, risen from the depths, slay Moby-Dick near the surface. (Another whale, a kraken, a giant shark, a giant ichthyosaur, an enormous sea serpent or something else.)
How would Ahab react?
Would he fly into a rage because another creature stole his revenge, or would he simply be satisfied that the White Whale had finally been killed?
My personal guess is this: at first Ahab would be furious and order the crew to pursue this other beast. The crew, horrified, refuse to chase this new horror. Ahab would rage, accuse them of mutiny. At this point Starbuck would take over. "It's one thing to pursue a whale with godless obsession, but quite another to lead a whaling crew into the jaws of an unknown sea devil." (Forgive me, I can't write dialogue worthy of Melville, but I imagine Starbuck would say something along these lines.)
Ahab would be confined to his cabin to calm down. He would spend hours raging there, threatening to kill everyone aboard.
Eventually, Ahab would calm down and rationalize the whole affair. He might even come to regard this new animal as a kindred spirit or somekind familiar. In his delusions of grandeur, he might even convince himself that his own thirst for vengeance somehow summoned this beast from the deep like angel of revenge.
The way I see it, to Ahab Moby-Dick is a some kind of avatar of God/Fate. If another sea monster could challenge the White Whale, Ahab might see it as proof that there are metaphysical powers arrayed beside him in his war against Fate.
Once the crew is convinced that Ahab has regained his composure, Ahab take over again He orders the Pequod to return to port. Ahab spends the rest of his life as a whaleman, always hoping that one day he might catch another glimpse of the creature he now thinks of as his brother.
Of course, I could be completely wrong. The White Whale is not Ahab's obsession simply because it is the uncrowned king of the seas, but because it wounded Him. So Ahab may not actually care whether Moby-Dick is the biggest and most terrifying sea monster in the world's oceans. So maybe he would only be angry that it wasn't him who killed the Whale.
Sorry for the fan fiction-esque scenario but it's a thought that's been lingering in my mind.