Laurin1, like you, I had no problem creating multiple groups, but each device could only belong to a single group. For instance, if my Dot was in the "Downstairs" group, it could not be added to my "Everywhere" group because it was grayed out.
Thanks so much for posting your solution. After months of banging my head against my desk, I tried it from my mobile device instead of the computer and it works perfectly!