I thought about doing this but read that voltage fluctuations between PSUs could potentially damage your computer components, so I decided against it. Remember, your GPU is getting power from the PCI-e slot too, so you can never have it powered totally independently without something more specialized.
You're better off with a bigger PSU. A good quality, efficient PSU is a good investment as it can last a long time. My Corsair HX620 is going on 5+ years now, and lately it has been constantly loaded while bitcoin mining.