Hi.  The only route to doing this with Sonos would be to use Ports, which would be very expensive.  I could not possibly be a bigger Sonos fan than I am, but given where you are starting from, and what you want to achieve, I would buy four Amazon Echo Dots, preferably when on one of their frequent offers, and connect into an input on each of your amps.  

This answer assumes that you live in a country where Amazon Alexa is available and that you are happy to use Alexa.

Further point - I believe Echo speakers are Spotify Connect enabled, which would mean you could play to the speakers using the Spotify app on your phone.  You had better confirm that though.

If you get a good offer on the Echo Dots this might cost you only about £/$120.  Worst case £/$200.

I am a big fan of the Echo devices for all they can now do for a legacy style HiFi system that makes Sonos redundant, while retaining legacy kit sound quality - EXCEPT for the kind of use case you are referring to where no one still serves that case better than Sonos does.

The Echos will serve, but it will be nowhere as slick/fast as Sonos. Unfortunately the entry ticket to that is the expensive Port for each room. Perhaps a couple of Dots can let you see if they suffice, but they probably will not if the use of multi room is extensive.

If all systems use a 3,5mm jack a Sonos Port connected to it (via an RCA to minijack) in every room would get you the same (or different) music in every room. You’d have no volume control though.

Yes you would, with the Ports on variable level setting. And the receiving kit can also have a Aux in socket pair for this to work.

Ah, you’re right. Didn’t realise this as my Connect is on fixed.

Thank Y'all for the quick and thorough responses. Yea, $450 per room for a port, may be more than I was looking to spend. Two of the rooms have the nicer stereo equipment, where as the other two rooms I could consider switching to Sonos speakers. If I got two ports and then two Sonos speakers I could then stream in all 4 rooms, correct? Also would this setup would allow me to have variable volume in each room? That is definitely important to me. 

As far as sound quality goes how do the echo dots compare to the Sonos port? Are both options just going to be the "very high quality" Spotify streaming quality sent over comparable 3.5mm outputs? Or does the Sonos port offer a significant upgrade in the quality of its output signal over an echo det? Also does the 4 echo dot setup offer variable volume control in each room? 

Finally, I have two existing Google home minis. I have been frustrated before trying to get them to play the same music in two separate rooms. Maybe I was using it incorrectly (I got quickly frustrated and didn't really try to figure it out as it wasn't important at the time.) but is it possible to achieve the same thing as 4 Amazon echos with 4 Google home minis? 

Thank Y'all again, this has been very helpful, Will

To the first, yes, this is a good approach and yes to all the rest of the questions.

I have used both the earlier version of Port and Dots as sources and I have found no audible differences - what the Ports offer is much slicker multi rooming, that is for sure.

No idea about Google Minis. I have Echo Show units wired to the line in jacks of my Sonos kit, and I find myself using the Sonos controllers for multi rooming. All other times, I use the Echo Show - either via voice or via Spotify Connect, bypassing Sonos controllers.

The sound quality will, I believe, depend much more on the audio equipment you have than on whether you use a Port or a Dot to feed it.  The Port would be better, I am sure, but whether enough to to justify the extra cost is a very individual and personal decision.

@Kumar is correct that the Sonos user experience would be superior.

I use the multi room feature extensively, just not for multi rooms where I don’t use it at all!

To clarify:

My 6 zone set up has 5 zones for a open concept living/dining/kitchen/bar and adjacent patio. The sixth zone is the bedroom.

I never feel the need to have all 6 zones playing the same music - in fact, my bedroom is a Echo wired to a Sonos Connect Amp that always plays standalone, and the Sonos unit could well be any other third party make amp.

However in the open concept space I often need more parts of it filled with the same music, in perfect sync, but with separate volume controls to fill as much as the space as needs filling so that the music does not sound too loud in any part of the space. So I may group as many as 2 to all 5 zones there from time to time based on how the space is being used and Sonos supports this better than the wired to Sonos Echos presently can.

If I were in a house with rooms that are in fact rooms and not zones in a large open space, I doubt that I would feel any great need for multi room, and, as a consequence, for Sonos.

I therefore suggest that the OP be sure that his need for multi room is real and will persist once the novelty wears off.

As to the sound quality question - if analog out of the Port is used, I see no technical reason for sound to be better than from an Echo Dot. And neither do I hear any. If the digital out on the Port is used feeding a very high end DAC, sound quality may be better, but I have not seen any such surviving a strict blind listening  test.

I suggest you get a handful of Chromecast Audio streamers. Note Audio, not the normal Chromecast, these are no longer in production but you can fund them used or refurbished online. With your collection of existing amps this gives you an inexpensive and easy to use multiroom system that supports Google Cast and Spotify Connect.

Yes.  The easiest way would be by voice, 

I know nothing about Google Minis, but would be amazed if they can’t do the same. 

I am sure we would all be interested to learn which solution you settle on and how it goes.  There are many valid suggestions on this thread.

I used Chromecast Audio when they were launched; they were the first devices to show up the silly pricing of the Port. I gave up on it because it was too much of hassle for me to have to access the phone each time I wanted to make any intervention on music play and I did not find the app to be very easily useable. 

YMMV, but it may not be worth the trouble.

PS: at that time, there was no Spotify Connect.

Works fine with Hifi Cast…. Which, IIRC, only cost a few UKP to get rid of the ads.

I think it improved since then. I own 5 or 6 of Chromecast Audio's, used them in my former house. It's a neat little streamer especially when connected via toslink optical to a DAC/amp with digital input.

The reason I have Sonos now is that i moved to a house which had several zones built in already, with Connect:Amps to drive them.

To me, there are (dis)advantages to both. I play music from my own network server (lossless flac), use Plex, streaming via Spotify and listen to local radio stations.

The Sonos app is nice and makes it easy to group/ungroup zones. The wired connection is robust. But Sonos is weak for own media, lacking in support for NAS drives and highres audio. Ans while the app does a good job to integrate everything, it is very very basic in terms of music discovery and metadata. The native apps from Plex and Spotify are much more enjoyable to browse a music collection.

Chromecast Audio allows me to use Plex and Spotify natively to stream music to multiple zones (to Sonos only one zone). But to group/ungroup zones you have to enter the Google Home app, which is more hassle.

I think CCA could be the superior streamer for a setup in which grouping of zones is relatively fixed. So your open plan house would actually fit this usecase very well. For me, I'm a bit on the fence right now. Probably I'll stick with Sonos for now, but hesitant to upgrade until I see true improvements/benefits in the S2 software and get a better feel of where the company is going.

The open plan needs different zones/zone combinations at different times, and Sonos still does this better than anyone else.

On a standalone basis with even high end systems, Echo Show 5 wired to analog line in jacks is excellent and cheap enough to be dedicated as a source, leaving its other Alexa gimmicks unused. With a My Media for Alexa instance, local NAS is covered by it, as are Spotify/Amazon Music/Apple Music. And all, with album art and more voice control than what Sonos offers.

I don't drink the Hi Res Kool Aid, so that is no miss in my book.

Echo lends itself to another cool addition - a cheap old Dot can be put to dedicated use as a voice command post at the other end of the open space, where it routes all commands that it hears to a chosen, wired to line in jacks Echo elsewhere in the space, to avoid having to shout across the open space which is a nuisance to do when music is playing.

And My Media for Alexa is also available for Raspberry PI that can be dedicated to it, with music on a USB stick containing ripped CDs/download files plugged in, and left on 24/7 anywhere in range of the WiFi network. Echo can then command it to play via voice, with album art as well where Show units are deployed.