Yes. Easiest way (least fidelity loss) would be to use latching relays in a switch matrix.
Can you amplifier handle 2 sets of speakers at one time? If they are 8 ohm speakers, then your amp would see 4 ohms. Is it rated for that?http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=255-1900-ND
You apply your stereo source signal to pins 4 & 9http://media.digikey.com/pdf/Catalog%20Drawings/Relays/TX-PCBd-bottom1COIL.jpg
pulse of current from 1 to 12 connects pins 3/4, 10/9
pulse of current from 12 to 1 connects pins 4/5, 9/8.
Pretty much use an H-Bridge circuit for that.
Latching relay, so last direction commanded stays, even after power down.
So, get 6 relays.
Connect your input signal to pins 4 & 9 of all six (+ & -)
Connect your room speakers to pins 5 & 8, one pair to each room.
Then have your arduino make the connections between 4/5 & 8/9 for the room you want on.
and 3/4 & 10/9 for the rooms you want off.
Make sure your amp can handle 2 or 3 sets of speakers connected together.
If not, then you need a different approach, such as connecting the relays to the inputs of an amplifier for each room.http://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-383
Maybe something like this in each room as volume controlhttp://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-560