create a second user in the system (shelter) with its own addresses - but it would still be all or nothing.
Slightly kludgy, but another approach is to have contacts owned by a separate Contacts/Dialer app instead of the system - OpenContacts | F-Droid - Free and Open Source Android App Repository
Nice feature in iOS 18. Guess Google will introduce this themselves in Android and it will trickle down to the ROMs.