There are several Navigation Performance Minima defined by ICAO.
For example MNPS for the Atlantic Oceanic is 12,6NM later in 95% of time.
Since e.g. the Atlantic is a very bussy airspace, but without ground based Navigation Aids and communication to a controller is difficult, there is a incentive to improve the nav perf of aircraft.
There are several regions (Shannon, Gander, New York, Santa Maria, Reykjavik) of wich a at least one has already adopted a MNPS 10 instead of MNPS 12,6.
The goal is to eventually reduce it to MNPS 4, but that might take a while.
In addition to that there is also vertical seperation, which up to FL 285 is normally 1000ft (semicircular flight rule).
From FL 290 it is 2000ft, exept in RVSM airspace (reduced vertical seperation minima), where it is 1000ft up to FL 410.
Above that vertical seperation is always 2000ft.
So a lot of planes fit into a quite small volume. Planes which can not satisfy these criteria are not allowed to fly within them.
Since I'm in the process if learning this stuff, I might have missed something or got something wrong, but it might give you an idea.