Most of the standard pressure switches have a fixed deadband (range between on and off setpoints) and adjusting the screw just moves this range up or down (so for example 90-120psi on/off could get dialed up to 120-150psi). There are plenty of more sophisticated control setups used on industrial equipment, but of course those will cost more.
Does your compressor have enough flow that it can keep up with whatever tool you want to run on a continuous basis? If not, your pressure will drop below 110psi regardless of the pressure switch setpoints.
Have you considered using a pressure regulator?
The right answer, this being a garage/tool forum and all, is a much larger 2-stage compressor with a regulator set at 110psi. Then you're at 110 all day long, no higher and no lower. And you'll wonder how you ever got by on whatever girly-man compressor you are using now
