No. In order to see each ‘room’ in the Sonos app, each ‘room’ would need its own Sonos Port (with an amplifier) or Sonos Amp. 

The cheapest way, without ‘seeing’ each room, would be to add a Sonos Port to your current amplifier, and then you’d be able to play one concurrent stream like you do now. If you wanted different potential streams for each room, you’d need to add a Sonos device for each. All Sonos devices (currently) provide a single stream. 

Get a Port yo hook to your current system as above. Use that to play the same music on all the speakers you leave connected to the existing amp/switch.

Get a Sonos Amp for each other room that you want to play different (than the amp/switch) music in. Wire the Sonos Amps directly to the speakers you want to directly control the source.

You can use one or more Sonos Amps, and you can connect (most likely) two rooms to any one Amp if the speakers are 8 Ohms.

Thanks for the suggestions!  I definitely will get a Port to bring Sonos as a source into my AVR.  I’d like to keep all the speakers connected to the AVR as the main source and amp so I don’t think adding a Sonos Amps for each zone will let me do that.  It appears there are some intelligent speaker selector boxes that allow independent volume control and a remote app to control selection and volume.  I won’t be able to manage it all from the Sonos App but it might be a workable alternative.