Short answer no. 

I know that you’ve discounted this but could you create an SSID & Password that is common across all of your Access Points just for Sonos devices to connect to?  This would still enable you to tether your other devices to a specific AP, whilst having consistent Sonos wi-fi connections.

Can an access point have more than one SSID for the same frequency?

Depends upon the AP, a lot of them have a capability for multiple SSID or a guest SSID.

I have a network with multiple wireless access points (APs). But all of them conspire to expose a single WiFi network/SSID with a single acceptable password. And yet when I move around the house with my phone and roam, I constantly am needing to repair the two devices. Super frustrating.

The iPhone handles the roaming well (it always has); it’s the Sonos Roam which seems to consider each of my APs to be a separate network or something. 

If my phone is connected to on AP, but my Roam sees another AP as stronger and connects to that, is the Roam incapable of communicating with the iPhone?

There’s a better than average bet that your devices are splitting up your network to different subnets, and Sonos requires a single subnet so that all speakers can not only communicate with the controller, but also each other. It’s not just a single SSID that is key, it’s a single subnet. 

My phone retains the same IP as I roam around the house (switch from one AP to another), so I’m not convinced it has to do with subnets on my main WLAN. However I have been on Unifi/Ubiquiti forums and apparently this problem is not limited to me, by a long shot.

When the Roam is moving around the house while playing streaming music, is it losing connection to the internet?  I understand that your question was about your phone/speaker connection, but I’m wondering if the issue is less about your SSID/subnet and more about the Roam losing access to WiFi entirely.  Not sure, but perhaps the Roam just isn’t built to switch to a different AP as easily/freely, taking the strongest connection, the same way your phone does.

A related question, but when the Roam is stationary at one side of the house with a solid connection to one AP, can you connect to it with  your phone on the other side of the house, connected to a different AP?  If you can, then the issue isn’t SSID/subnet.  If you can’t then it seems like that would be the issue.

But I am not that great at networking issues, others can advice better than me.

RE: you question #1, the Roam does seem to be ‘greedy’ in the sense that it doesn’t like to give up an AP connection even when moved closer to a different AP. So in that sense the brand name ‘Roam’ seems quite ironic.

Answer to question #2: yes, currently my Roam is the far end of the house and I know it’s connected to a different AP than my phone. The Sonos app connects with it almost instantaneously, so it’s not a question of splitting across APs.

However I do have more news: I connected both my phone and Roam to my IoT SSID (not my main SSID). Same APs doing the broadcasting, different IP address space, and apparently different inter-client communication rules because now the phone connects pretty reliably and quickly. So for now this appears to be down to differences between my broadcasted WiFi networks.