I think there are systems that let you send the same source to many different channels (more or less targeted at what you're looking for), but I'm pretty sure you are gonna need a seperate amp for each room (along with a media receiver).
I have also seen some systems (can't remember the name), where they make one hub system, and a series of "extra units", each including both amp and speaker. I have no idea how the sound quality is, but I can't help thinking that you're paying overprice for the ability to plug and play each unit, and the sound suffers from it.
Brands that come to mind that you might want to check out are Sonos (slightly expensive) and Logitech (less expensive, but might be poor quality)
You need a mulit-room system, some AV receivers have this functionality but usually only for a second room. To do this properly your probably gonna have to spend quite a bit of money, what is your budget?
It will probably entail using a source control unit hooked up to at least 4 amps (1 for each different room), your probably best going to a specialist AV company for advice. This is assuming you want to use different sources in the different rooms. If you simply need to play the same source throughout the house then you will need a pre-amp capable of feeding power amps for each room.
Alternatively you could look into using wireless streamers hooked up to a main source, such as a PC. Sonus offer such systems but for 4 rooms your probably looking at over £2000 (i could be wrong though). If your having the speakers from each room wired up to a central point then there's little point in this route though.