Do you want independent volume control in all of the rooms?
Do you want in-room control of that volume, or do you want to have to pull out your phone to adjust volume in every single room?
What wiring is at the wall plate location in each room? Is it cat-5e or similar network wiring?
There are tons of distributed audio systems available. A often recommended system is from Home Theater Direct...
Just as an example. 12 zones with full control, keypads, and phone control runs a bit over $4,000...
You can dumb down systems quite a bit, but this would be kind of typical for a quality distributed audio system. You want amplifiers for all 11 zones, which typically means getting two, 12-channel amplifiers.
But, you can get those on eBay as well.
At under $300 each, a couple would cost you under $600. So, that gets power to the speakers.
Then you need a controller. Going back to HTD, you can pick up their 12-zone controller, by itself, for $1,400...
and their smart gateway (I believe this is required)...
So, about half the price point, and you get all the rooms under iPhone/Android control. You can add individual keypads to the system later on if you want to.
This will give you volume control and source selection, but you will still need to add sources. I do like Sonos as an option. But, you could get by with just one or two Sonos players and call it a done deal.