While you can sign in to your Spotify Premium account on as many devices as you like, you can only listen on one device at a time.
Unfortunately you can only play music on Spotify Premium on one device at one. This is to stop multiple users sharing one account. You can sign in to your Spotify on as many devices as you like, however if music is played on another device, it’ll pause any other device currently playing. Up to 10,000 tracks can be downloaded for offline playback on five devices.
For family members under the same roof, Spotify Premium Family is a great option for up to six users for $14.99. Each user gets their own account, so personalized recommendations stay unique.