This view of the future isn't really a third model, but a complication of one of the other two. It's just the idea that events have more than one cause and to change the future can be a complex undertaking. Avoiding a negative future is more difficult than just assassinating one person. Ensuring a good future equally involves chains of smaller events that have to happen or be avoided.
Trapped in History
I think his view of the future has become popularized, oddly enough, by seeing the future from the past. In other words, time travel stories. A character travels back in time and the problem becomes, not predicting the future, but how the choices that character makes interact with a future we already know.
In that sense Future as Web is most commonly related to a Future as Fate. The events in the time traveler's future are inescapable because, well, that's our history. But the Future as web isn't about that so much as a means used to prevent any change from happening. Oh, you think you can stop WWII from happening just by killing Hitler? Well, you actually killed a body double who was conspiring to replace Hitler. Or, you miss your shot and make Hitler more paranoid and dedicated to his war aims. If the Future as Web is used with the model of the future being fated, the layers of causes act as a buffer to any change to the future that's already known.
Alternate Histories = Future as Possible Paths
There are some examples of the opposite, though, basically any story where history as we know it is malleable. This is frequently seen in time travel stories where something has been screwed up by the traveler and they need to make things right so the future happens as expected. A familiar example is Marty McFly trying to get his parents to fall in love. This is the Future as Possible Paths, because we see, even when Marty succeeds, he returns to a different present. Again, Future as a Web is not in reference that he could change the future but the idea of the interconnectedness of all the causes that result in what will become the future. It isn't as easy as just getting his parents in the same room, he has to deal with Biff, the principal, and the time crunch of scheduled events.
The Future that's Bigger than You
Because Future as Web is about something harder to change with many interconnected causes , it's usually about something bigger than any one person. It is a kind of Grand Destiny. Wars, the succession of Kings, great plagues, these are foretold. To avoid destiny takes more than a single act. The seer will still be affected by future events but this future isn't their personal fate (even with Marty, there's also the existence of his siblings hanging in the balance). Future as a Web is less "how do I prevent the halfing from stealing my purse" and more "how do we ensure the Empress Dowager is dethroned?"
I think these Grand Destinies can come into play either as adventure hook prophecies that players hear, or when players desire to make a big change in the world and go to someone with sight of the future to give them guidance on how to achieve it.
Rather than a table here to generate particular Grand Destinies, I'll just say they should be things that happen in a sandbox but not require players to interact with them. My post here looks at some possible examples and one way of handling them, escalating things over time if players don't get involved. Contrary to my advice in the Future as a Possible Paths post, because these destinies are harder to avoid, I don't think they should be related so closely to things the PCs own or people they know. That route leads to frustrating railroading.
Now, how you model predictions of these magnitudes depends on which of the two views of history you are using.
If Future is Fate, I think you can choose a destiny and several smaller trigger fortunes. Then, use Zak's method of allowing players to say when a foretold event happens except that those smaller fortunes either a) have to happen in a particular order, or b) need to happen simultaneously.
Example: The Empress Dowager will lose her throne when a feast is prepared but not eaten, a rope snaps as music plays, a crown rolls across a stone floor.Here, the predictions become a kind of key to the prophecy; if players can arrange a situation where they all happen, then the prophecy comes true.
The PCs realize the heir apparent will be hung for the pleasure of the Empress and her court and wish to prevent it for their own reasons. They interrupt the execution/banquet, manage to snap the noose, and roll the hereditary Great Crown they've recovered across the floor for all to see.
The courtiers and generals present are shocked and pivot to support the heir.
If the Future is Possible Paths, it becomes trickier (for the DM at least). Because prophecies are just one possibility, players can just work against them to make them not happen. There isn't the sense of "stickiness" or difficulty in working against destiny. Here's an idea for a way to allow players to do what they want and still give that sense of the complexity of changing what is destined:
Usually players will be trying to prevent foretold events, because otherwise they could just stand back and let them happen. For a particular event of great importance that players want to stop, come up with 4 smaller events or preconditions that will affect its likelihood. Let these be discoverable by players-- wise npcs advise them, they find them in books, they see them in dreams. When it comes time to see if players can prevent the destined event roll 1d6, 6 = yes. Modify the roll by +1 for each of the smaller events that PCs managed to make happen. I think I would make this transparent to players, to give them a sense that they are up against that die roll and destiny itself. But allow players to come up with additional factors that would result in modifiers.
Example: Prophecies say the Empress Dowager will rule for a 1000 years.To liven it up, agents of the parties desiring the prophesied outcomes could actively work against the PCs-- the cultists wishing the World Plague to occur, the rebels desiring the Elf-Dwarf War. If this works as I envision it, any time Players chafe at a grand prophecy could result in a whole mini-campaign of them trying to overturn it.
PCs learn that getting her generals against her will make a difference (+1), they learn that the Great Crown that true Imperials wear has been missing (+1). They learn the heir apparent is secretly held captive in a tower (+1). Coming up is an important political/religious ritual where the Imperial power is reaffirmed (+1).
They speak with the generals, even performing some tasks for them to win them over. They rescue the heir apparent and recover the crown. They plan to present him to the court on the ritual day. But, worried this won't be enough to shake the 1000 year reign, they decide to search for evidence of the unlawful way the Empress Dowager seized the throne and present it to all as a magical projection (+1).
That is enough, the heir apparent takes the throne. The prophecy has been avoided.