Realistically you want a surround sound AV receiver with two zones and 9.1 channel setup for the TV room, then a second amplifier to power the other rooms.
The receiver will feed a single source to the three other rooms.
Do you have volume controls in those three rooms or are they just directly wired back to the equipment location?
I'm assuming you don't have volume controls, which means, at the very least, you will need a speaker selector/volume control unit for those three rooms like this:
Find many great new & used options and get the best deals for Niles SSVC-4 Four Pair Speaker Selector w/Volume at the best online prices at eBay! Free shipping for many products!
www.ebay.com
This will allow you to turn on/off the individual rooms and adjust volume for each room.
Pair it with a decent amplifier and call it done.
If you want to actually have those three other zones be capable of playing their own source, at different volumes, and control it from a phone and play different things in different rooms, then you might need something like this from HTD:
DetailsCat 5/6 cable NOT requiredIt is possible to control our Mid-Level and Lync whole-house audio systems from any iOS or Android smart phone or tablet using your existing WiFi network and our free apps. If the difficulty of running Cat 5/5e/6 cable to Keypad locations has prevented you from...
www.htd.com