social standing is even less zero sum than capital. if I choose to respect you, that doesn't mean I have to kick the next person I see in the groin.
edit: sorry, now I see. how can you lord your wealth over the peasants if they are as rich as you? why should we as a society care how much you get you put yourself above others for no good reason?
The classic terms are sufficient. Upper, middle and lower class are all inherently relative terms. Everyone cannot be "upper class," or middle, or lower.
This is about relative social standing. Which is zero sum.