Boost +12v from ATX PSU to ~13.5-14.5v
Typically the feedback is taken from the 3.3V output and fed back using a TL431. There might be a second TL431 for the auxiliary power supply. 

To change the voltage you would increase the series resistor from the 3.3V to the feedback terminal of the TL431/HA17431. This will increase the positive output voltages (usually the negative ones have fixed regulators).  

However if the power supply has overvoltage protection, as many (and all good ones) do, then you may trigger that and your power supply will shut down. Without a schematic it is going to be difficult to determine how to deal with that.