Yes, you can use as many sound cards as you want.
In Control Panel > Sounds and Audio Devices > Audio, you can select what your default sound device is. This is where everything goes unless you specify otherwise. For example, on my system I can select "SB Live Wave Device" or "nVidia nForce Audio" since I have a sound card and onboard audio.
If you just want to listen to music on your home stereo, that's really easy. You can just add a PCI card and hook that up to your stereo. Leave your onboard audio as the default sound device, then specify the PCI card for the sound device in your music software. For example, WinAmp's output preferences let you select which sound device to play to.
If you want to play games and have the sound come through the stereo, that's a little trickier since you can't specify the sound device for most games. If you have decent onboard sound, you can just plug all the speakers into your computer and set it to 4-speaker (clone) output to use the stereo and the computer, then change it back to 2-speaker output to turn off the computer speakers (or just turn the speakers down in the mixer).
There are also several ways you could patch your onboard sound together with a PCI card depending on what you're trying to do. You can set the PCI card as your primary sound device, then use a splitter to run the output of the PCI card to your stereo and to the input of your onboard sound. Then you can hook your computer speakers up to the onboard output and just use your onboard sound mixer to turn off your computer speakers.
Obviously you could come up with the best way yourself depending on what you want.