The usual advice is to use very little pressure, and if that doesn't work, a very mild and unaggressive razor. But the fact is that not everyone's skin can tolerate a third pass, and some of us have to settle for two. The problem isn't always bad tecnique or overly-close shaves; with each pass you scrape off a layer of the outer skin (stratum corneum) and people with paler complexions and blonde hair are especially prone to their skin getting sensitive and sore with more of that than they like. Guys with olive skin and swarthy black beards can often shave all day and feel fine. It's certainly the case that even a single pass shave with a proper razor will look fine through the work day, even if it feels a bit rough as the day goes on. I'm guessing that HR departments these days rather frown on inviting people to check out the smoothness of your shave at work, so that probably won't matter.
Of course, being SRP, I have to say straight razors are less irritating than DE shaves. The funny thing is, I've found it to be true!