Two PSUs are possible, but I would not try to combine them in any way.
First, when two PSUs are in the same path, any voltage difference between the PSUs will result in current draw. This is not only inefficient, but could damage whatever else is in the circuit.
Second, when a voltage is supplied by two parallel supplies, the current tends to go through one, rather than both. This means that one supply will do all the work, and could even burn out, while the other one just sits there looking pretty. Parallel supplies rarely work out.
Instead, you would want them to share a common ground, but separate the current paths as much as possible. This means that, while one PSU could power the Motherboard and any expansion cards installed, the other could power all peripheral components: fans, drives, card readers, etc.. If you're careful, you could even rewire your USBs to supply voltage with the 2nd PSU - reserving all the 1st PSUs available current for the MoBo/CPU/Memory/expansion cards.
There's another option. Take it to a qualified electronics tech. He could resolder the proprietary cables into a new PSU. Any qualified tech should be able to do it with just a solder pen, a voltmeter, a pen and a pad of paper. Darn nearly 100% of the time, a "proprietary" PSU is just a standard PSU with a couple of odd connectors attached.