It is one(ish) cup at a time, though you can simply make a stronger brew and split it between multiple cups (and then top up with hot water).
As for the pressure, I’ve never yet even come close to tipping the cup. The pressure you apply isn’t that hard, not as much as you’d use with a french press in my experience. I normally use a tall thermal cup with mine, as I tend to forget about my coffee. If I’m in no danger of tipping it over, you’d never tip a normal cup/mug.