Except that's exactly how it works. Your house has two live feeds coming in that are 180 degrees out pf phase with each other. When combined, they create a 240V total potential. Your stove, clothes dryer, and water heater all use 240V circuits. A 240V breaker is actually two breakers adjacent to each other (because each alternating 'blade' in your panel is separate phases) with their switches linked together, so when one trips it forces the other off as well.

To OP: you can get a 240 breaker from Home Depot or wherever, but you will also need to replace your receptacle with one that can handle the increased power as well as 240V. You will also need to upgrade to 12/2 wiring on that circuit most likely. Also also... unless you have a 1500W or greater PSU, it doesn't make a difference if you have 120 or 240. Also also also, you can run multiple PSUs with multiple 120V standard household circuits, just without a joined breaker they won't all trip together.