6-dimensional Half Life 3

The short version:
-The Borealis is the pivotal element of this story. Able to jump between universes but never find Earth, over the decades it has been adapted to interuniversal travel. It holds the key for the Combine to invade Earth, and thus is of great interest to both the Combine and humans, leading to a hunt.
-The player hunts down the Borealis using more refined interuniversal travel technology. Like the Displacer, but able to travel somewhere other than Xen.
-Instead of being linear, the player is free to hunt down the Borealis with their own strategy and pace.
-The biggest theme of the game is aliens, and alien worlds. Like No Man's Sky, except instead of being stupid and generating aliens on the fly with a crude method, aliens are generated partially by incredibly powerful computers simulating evolution with modern methods, and then the finishing touches are done by the gamer's computer.

The long version:

In this interpretation of Half Life 3, the Borealis still has half the crew alive, and is occasionally travelling to other universes, having to live off of whatever they can find as they are unable to find Earth again.

The game takes place in 6-dimensional space, with the familiar 3 spatial dimensions, but also 3 universal dimensions.
If one were to render the latter 3 dimensions, it would be a shell of universes surrounding Xen; and every point in this shell is an entire universe.
This is further explained here: https://pastebin.com/L0RCC03Y

The player acquires at some point in the game a portal gun, but instead of creating a hole in the wall you are facing towards, it translates spatial orientation to universal orientation and creates a tunnel facing towards the universe you're pointed at.
This would explain something of Half Life's canon: The difficulty of same-universe teleportation.
A "horizontal" teleportation would send you to the universe next to yours, a "upwards-diagonal" teleportation would send you to some other universe, an "upwards" teleportation would send you to Xen, and a "downwards" teleportation would send you god-knows where. None of those send you to the same universe, only a clever trick with upwards teleportation sends you to the same universe.
You cannot simply teleport from any universe to any universe, or at least you cannot do so safely; you must walk to such a spot that when you jump to the target universe, you're only a few metres above the ground level of whatever planet is available. Only a finite number of universes exist within your scope of travel, so there is not always a safe teleport destination from where you are.

Your goal, of course, is to track down the Borealis wherever it is in 6 dimensional space.
However, the Combine are also capable of multiversal travel, so they're trying to track down the Borealis too.
And the Borealis itself is often on the move, and modified to the point of unrecognisability, having salvaged mostly-biological components from hundreds of alien planets.

Unlike the Borealis, the player doesn't get lost, because their portal gun actually keeps track of where home is.
But however you track down the ship will probably be something crazy like detecting minor fluctuations in 6-dimensional space, so if you're near (close universally or spatially) to a place that was teleported to/from, you can detect that teleport.
The Combine, however, will use the same trick with you.

It's meant to be a game that's hard to win (you don't get guided through a linear campaign), but fun and interesting to play, since you're travelling through a multiverse.
Aliens are premade based on individually-acting cells capable of evolution (even simply implementations of this have produced really good results). Then the cells are turned into simple meshes and skeletons, but with lots of metadata to do with types of cells. Thousands of these simplified creatures then get shipped with the game, and the models are detailed and textured on-the fly. The game .kkrieger is a great example of how simple assets can be improved on the fly, to minimise storage space. Which is important, when the game has to have enough aliens that the player could traverse a hundred planets yet have a unique experience each time.
https://www.youtube.com/watch?v=CXTZHHQ7ZiQ is a simple example of cell-based creature evolution. Something using more cells, and more types of cells would be expected to fall even more in line with the real products of evolution. Bone would make a big difference.

As for the ending:
At some point, you'll be on a ship loaded with some of the most destructive devices and organisms the multiverse has to offer, now finally able to navigate since your portal device has the necessary guidance technology.
If the ending was multichoice, it could be one of the following:
-Expected ending: Explain that the Borealis must be destroyed to protect Earth, rigging it to explode and sending everyone home with your portal gun.
-Badass ending: Destroy all your portal technology as you stake out a spot in the multiverse for the ultimate showdown, letting the full force of the Combine fleet attempt to capture the ship, only to be torn asunder by alien weaponry and alien aliens. Only after losing hundreds of vehicles and thousands of soldiers would they find that you already destroyed the technology they sought.
-Genocidal ending: Attack the Combine Overworld itself, dropping Resonance Cascade Bombs to turn the entire planet's surface into an interuniversal warzone; like Half Life 1, but on a planetary scale.