You can if you have the right GPS receiver, ie. one that allows corrections from a Differential GPS transmitter (DGPS). These are transmitters located at specific points that broadcast timing corrections derived from the errors sent in GPS satellite broadcasts.
Any GPS receiver capable of receiving these transmissions and utilising them will use their data to correct the data received from the satellites.
This can offer accuracies down to about 10cm but the receivers aren't cheap and you also have to within the range of a DGPS station. You can get portable DGPS transmitters though, say for if you need it for automated vehicle control, eg. mining trucks, and you're not near a permanent DGPS.
They also have the same thing using satellite based DGPS called Wide Area DGPS, (also called Wide Area Augmentation System - WAAS) - but it's not as good as DGPS, you can get down to around 3m accuracy.
Ground stations broadcast corrections to an orbiting WAAS satellite, which then broadcasts a correction signal that any capable receiver can pick up and use.
Better than DGPS in the amount of area covered but from what I remember you still need the ground stations to be in the same global area as yourself, ie. ground stations in the USA broadcasting corrections to an overhead WAAS satellite are of limited value to a GPS receiver in Australia, (if it can see it), and vice versa.
A lot of low cost consumer GPS receivers can take advantage of that - depending on the make/model if you enable that setting you'll start seeing a W, (or something), next to various satellites on the display, eg. my Garmin Geko 201
has it (enabling it causes increased battery usage though).
While government/military systems can thread a needle from space, they don't think the civilian riff-raff need that sort of pin point accuracy ... Hence we don't get access to it.
Surveyors use very accurate GPS' all the time these days.