Hi Robin,
I assume that these are open hallways or stairwells of an apartment building.
Your best option is to recoat with a two part epoxy paint. These paints are site mixed usually equal parts hardener and paint. Since the existing (epoxy) walls have long since "cured" you can not achieve a chemical bond to the existing epoxy paint.
A mechanical bond will have to be achieved by sanding.
The existing epoxy must be cleaned, a solution of TSP
(trisodiumphosphate) should work well to remove most common dirt and grime (If the work site allows you might also consider a power washer) A solvent such as acetone can be used to clean off heavy grease or oily areas.
Create a key in the existing surface by sanding with 80 grit aluminum oxide sandpaper. You might consider renting a (powered) drywall sanding pole to save time.
Before you recoat make sure that the surface is dry, epoxy paint does not tolerate moisture during application. Do not apply it late in the day.
Your turn around time should be a matter of hours depending on the temperature and humidity levels at the time of application.
As with any chemical, Epoxy paint and solvents such as Acetone should be handled with caution and common sense.
Sounds like a pretty big Job.
Good Luck,
rmichael / pro painter