Thanks, jiripolivka. Sorry, my desciption is not very clear. My question is really: how do I send a stereo audio signal from the computer (or any device) to multiple sets of speakers? What audio amplifier would be best? Is it easiest to send the signal to multiple amps in series, using a common power supply?
(The bit about switching and volume control I would implement separately, possibly through a parallel port or local network. Also, perhaps there is a chip that will take a digital audio signal and convert it to analog (and amplify) it? As you can see, I don't know very much about audio circuits.)
If your task is so simple, then you can use the LM386 to feed each of speakers with ~ 0.5 W audio, through a volume-control potentiometer. There are many other good audio amplifiers, often sold as kits (Ramseykits, All Electronics, elexp.com) some with more than one watt of audio output. At MCM electronics I saw nice tiny 20W audio power amps.
The only task then would be to use simple resistor dividers from computer audio output(s) to each amplifier input(s). Volume control is either built in such amplifiers, or, you can use 10 kOhm audio taper potentiometers for it.
As I mentioned, for computer-controlled switching, 4066 or 4016 ICs are analog switches controllable by TTL inputs. To replace the ordinary potentiometers, there is a selection of digital ones; details in their data sheets.
Concerning the DC power supply, most of the above mentioned amplifiers use 12 VDC. A good idea is to get a good "large" power supply capable of several amperes of current, and with DC blocking capacitors of 4000 uF or more. Often you can expect some audible interference due to ground loops, etc. A good idea is to try connecting all devices including audio output jack shield to a common ground. As laptops and PCs use switching power supplies, you may need a filter to reject unwanted sounds. In my case, to listen audio CDs and DVDs from my laptop on a larger TV display with stereo speakers, hum and high-pitch sounds forced me to use small audio transformers to break the ground loop. Expect some experiments to achieve good results.
You may search suppliers of "professional" audio systems. For much more money you could possibly find almost perfect system ready for anything. Ground loop problems are sometimes solved by using optical fiber or balanced transformers. Start with simple devices and gradually try to use more complex devices.