If you try to splice wires together, you'll get in big trouble by confusing the regulator of each supply and possibly cause oscillation and make the transistors short.
Keep each power supply separate except for their grounds (black wires - tie them to a common ground). IOW, use one supply for your motherboard, another for your peripherals. Plug both supplies into a power strip, and use the power strip's switch instead of the computer's. The reason for this is because ATX supplies need a zero voltage on ATX connector pin 14 (green wire, opposite red wire and between two black wires - can get zero volts by shorting green to black).