The follow up question is whether or not you want to run something different to these zones or do you want them all to be mirrored?
The 3313 offers two additional zones of stereo audio beyond the main stereo zone. This will allow you to listen up to two different things, but it will be across a combination of rooms.
As well, you will have to deal with turning rooms on and off manually or by using volume controls in those rooms.
You will need some type of external amplifier and volume controls/speaker selector for the 8 additional zones.
You can use a single high power amplifier with a speaker selector, or split it out to impedence matching volume controls if you would like. This is about the least expensive way to do things. You would turn your Denon on/off with your smart phone and would need volume controls in the rooms, or a speaker selector/volume control box for the rooms by your Denon. It's not terribly expensive to do it this way, and works well.
IMO, it means you almost never listen to music in your home because it's not extremely user friendly.
Instead, I recommend a good controller and keypads in the rooms with a 8 zone preamp and dedicated amplification to the room. This is more expensive to setup, but allows you full control in each room. Each room gets a dedicated keypad which can turn the zone on/off, pick a source, and adjust volume in that room. You typically bypass the Denon altogether in this setup as it won't provide 8 additional zones of audio and stick with the 8 zone switching preamp.
You would run the output from that preamp to 16 channels of amplification. Discrete dedicate amplification for each pair of speakers which should improve reliability and overall audio quality in each of the zones.
Yes, it is more expensive, but when you walk into the kitchen, you press a single buton on the keypad on the wall and it brings up XM or your media server and starts playback. Your wife in the master bedroom brings up some music on FM, while one of the kids brings up their MP3 player. When done listening, they each just press the 'off' button and walk out of the room without impacting anyone else in the home with their listening.
Every family is different in how willing they are to work with things, but I know when I've seen the first method installed, it was under-utilized due to the headache of having to go back to the basement to start things up, or because every room would come on at volume... or it was just to complex for most of the family to use.
In contrast, my 3 year old son would turn on XM radio before he jumped into the bath and turn it off when he was done.
So, yeah, budget comes into all of this significantly, and properly configuring a 8 zone setup can be difficult if you need to wire everything.
WORTH LOOKING AT SONOS in my opinion as well. All phone/IOS controlled, but wireless and versatile for the money.