I don't own a HomePod so I don't know how it interfaces. I am guessing it may need to be controlled by a device signed into an account and be controlled by that device (such as an iPhone), but I really have only ever seen one in pictures.
Urqhart1244 says you get up to 6 streams, but what https://support.apple.com/109339 actually says is, "With an Apple Music family subscription, up to six people can enjoy unlimited access to Apple Music on their devices." "People" in this context means Apple Accounts since Apple's system is designed that each person has their own Account.
Make sure that each family member has a unique Apple ID --> https://support.apple.com/HT204976
- "If you want to share purchases or subscriptions with family, use Family Sharing. Each person should use their own Apple Account.”
I can't find any official Apple statements about the number of streams you can have going on a single account at any one time but there are many many community posts from very knowledgeable users saying it can only be one at a time. For a given account if you start playing on one device and then start streaming on another, the first stops playing.
Since there appears to be a difference in interpretation here I suggest you ask Apple itself:
This support page has information about contacting Apple support and service ➔ https://support.apple.com/106932 If live support options (chat and/or telephone) are available they will show near the bottom left.
- Telephone numbers may only work when calling from the same country.
- Chat options (telephone numbers appear as active links, not plain text) may depend upon cellular connectivity. If a number shows as an active link, click on it to see additional options.
- If chat is not available on the top level support page, try selecting your hardware and narrow down your issue to see if a support article offers a support link offering chat. For example, the contact support link on this page https://support.apple.com/119902#zerobalance offers a chat link about emptying account balance even on a computer where the top level page does not offer any chat.
With an iPhone, iPad, or Vision, you may be able to chat using the Apple Support App if it is available in your country —> https://apps.apple.com/app/apple-support/id1130498044