VERY IMPORTANT:
Impedence matching!
Speakers draw a certain amout of power and when you put more and more speakers together they will (litterally) suck the life out of a amplifier if you don't control the power flow. It is possible, that the volume controllers in the room have this technology, called impedence matching, built into them. But, perhaps not. To find out, you will need to pull one of the volume controls out of the wall and see exactly what brand/make/model it is and then either ask, or go to the manufacturer website and read the specifications.
If it is not impedence matching, you will need to pick up a impedence matching speaker selector. They are about 30 bucks or so online to handle up to 4 pairs of speakers off a single amp. They also have versions to handle more pairs of speakers if you need it. You didn't say how many rooms have speakers though.
So, here's how I would do it on a budget.
amp (with speaker selector):
http://cgi.ebay.com/Sonance-Sonamp-260-and-SS6-6-Speaker-Selector_W0QQitemZ5843744314QQcategoryZ39783QQrdZ1QQcmdZViewItem
If you can get that for under 150 that's really solid.
Search eBay for Sonance Amplifiers which are designed from the ground up for distributed audio.
Speaker selector - either Sonance, or a Hometech speaker selector will work well.
1. Connect the tape out (record out) from your A/V receiver to a decent external power amp.
2. From the power amp, go into the speaker selector.
3. From the speaker selector, tie in all the rooms with speakers in them.
When you pick a source on the A/V receiver, that source will go out to all the rooms, but because you have the speaker selector right there, you can turn those rooms on and off individually - very nice. Plus, the external amp means that the house system won't affect your primary system at all.