Nintendo's Latest information about Animal Crossing: New Horizons ,
We already know the game will support up to eight players and four residents simultaneously, a rather sizable chunk of writing at the bottom of this page touches on the finer details about the user limits online and per console. Within the paragraph is a special note (as highlighted below). As you can see, you'll be limited to one island per console, irrespective of the number of user accounts or copies of the game you have.
Disappointing news as this might be to hear, this isn't exactly new. Past entries have also had limitations like this. For example, the GameCube release restricted four local players to a single town. In the Switch release, you won't even be able to bypass this restriction with an SD card swap, either, as save data is stored internally.