Actually, you can split the signal, do it all the time in HT setups. Make sure the first splitter (the one connected to the computer) is a stereo one and 3.5mm to 3.5mm, since the center is carried on the other channel you don't want to lose it. The second splitter that will be plugged into the 2nd sub will depend on what kind of input jack it has.
As ien2222 say you can do this. I would put the splitter at the closest woofer to reduce the wiring at the sound card. If you don't already have the second woofer you might get a better result by simply replacing the woofer with a better one that has the bass you want. Using two different subs can be tricky as they don't product the same sound the same way.