Yes to all.  Multi-room audio is the raison d'etre behind Sonos.

How does the amp power the rest of the existing sonos system?  If everything is wireless, that is?

The Amp doesn’t “power the rest of the existing sonos system”.  The Amp would power passive speakers which are wired to the Amp’s speaker terminals.  

https://www.sonos.com/pdfs/quickstart/amp.pdf

So “Yes to all” isn’t exactly accurate since I was asking how to get more volume out of the existing sonos system.  It’s just not sufficient for the space… thoughts?

What type of media do you normally play? Is this a music venue or a TV/surround venue?

Private party space ~2600sqft main area is ~1200sqft w/ several screens two smaller spaces ~700sqft each to the left and right of center.

Think like the sort of place you’d get a group of corporate guys together to watch MMA fights where you want to hear flesh hitting the mat and have it interrupt your conversation.

No, “Yes to all” does apply.  You can add the Amp and group it with the original room to add volume.  

Note: Any grouped room will have a slight lag for TV sources.  Music sources will be in perfect sync. 

But if I’m reading you correctly the amp does nothing for the existing system, it’s just basically going to power third party speakers?  I was looking for a way to make the sonos system a little less anemic without augmenting with other systems (may as well go back to a board and set something smart up in front of it and ditch sonos entirely)

There is no way to ‘increase’ the volume put out by Sonos speakers that have built in amplification in them, other than turning up the volume for each ‘room’ they’re in. If you feel they are ‘anemic’ you probably need more speakers in that space. 

Remember, there is a max in a Sonos system of 32 speakers.

it really seems like Sonos is not the option for you, you seem to be looking for more of a public address system with more speakers. 

That’s what I’m coming to realize as well.  It’s fine for four or five people watching a movie but really not a good solution for a big space with a lot of people in it.

Probably why their marketing is for ‘whole home audio’ and not ‘whole venue audio’.

Fair enough.  It’s a small private venue and the PA I had in place last month was dated so I was exploring this.  Was hoping that this could work out and be an easy to manage intelligent solution but I guess it is what it is thanks for the help guys.

Anyone want to buy some gently used Sonos crap? lol

I completely understand the desire, but at its core, it feels like Sonos doesn’t fit the bill. YMMV, sound is always a personal thing.