Hi,
yes, you can do this 
I do exactly this with my wife and daughter and Apple Music Family.
basically load the Sonos app on all the devices and log into the Sonos system with the Sonos account.
in settings, select “Services & voice”, here you can add separate Apple Music accounts.
we have 3 added
Apple Music : Me
Apple Music : Wife
Apple Music : Daughter
then when selecting “Apple Music” from the Browse Tab it should have a name there…. You can switch the accounts by going into Apple Music in Browse and then selecting the name below “Apple Music” on the top of the screen, select the down arrow and it shows all the accounts.
this works great for the Sonos App, one gotcha is that Alexa can only work with one Apple Music account. So if you use voice and Alexa to play music, it is the account that is in Alexa that will be used….. unless this has changed recently.
I have a multi-room setup where the kids all have a Sonos1 in each bedroom. It currently works well with Spotify Family as they can all stream their own playlists via Spotify App.
I took out a trial of Apple Music (Family account) and I'm considering switching to that service instead.
The Apple Music App only supports Airplay to newer speakers like my Play5 although the Sonos app lets them access their individual speakers.
However Sonos App appears to only allow 1x Apple account to stream (mine is setup and working). How do I set things up to allow the kids to stream their own music & playlists to their own speaker?
Add their account information to the Sonos app. They can switch to their account using the dropdown at the top of the Now Playing screen.
Use multiple accounts for the same music service
Thanks BMF - that worked a treat!
I was missing that we needed to add the multiple accounts individually from each iphone so it tags in the correct apple ID.
Delighted with this.
