Two 12v Power supplies in series?
Probably.  

The PC power supply (-) lead will be connected to the Earth terminal of the AC Mains plug.  The other supply may be isolated from the Earth terminal - or may not.  

If the (-) terminal of the other supply is in fact connected to the Earth terminal, it's usually pretty easy to open the case and separate the (-) terminal from the Earth terminal.  

Then just connect the two supplies in series.

I'd be tempted to install large diodes in anti-parallel with each of the outputs of the power supplies.  That is: Cathode to (+), Anode to (-).  The diodes should be rated for the full short-current rating of the power supplies.

The purpose of the diodes is to limit the amount of reverse voltage applied to the output of whichever power supply goes into current-limit first.