You shift the world in relation to whatever is the active camera essentially. If you need you can implement some extra logic to track the player position in relation to the world as it would be if it wasn't shifting, if you will.
I'm sure there's a way to make this work for multiplayer too, but I'm inclined to assume it would be a bit more complex for it, sure. On that note, each game client would be shifting things relative to the respective player so in that sense it would probably be no different, actually. Unless your talking split-screen on the same system.
And your server client, depending on how you program it, might not need to deal with any world shifting at all.
Also note that when I say shift the world, I actually mean you move everything, player too, but if the player is moving one way and everything else gets moved the opposite way, you have to be careful to not introduce issues such as the player suddenly seemingly moving too fast or instead stuttering or such.
Easiest might be to have things to interact with in your world while player is essentially not moving, picking something up, opening a door, etc. A good moment to shift then. Or if it's a racing game, have a pit-stop of some kind, a gas station for an example.
