How can I obtain more Nintendo Switches?

After opening Nook’s Cranny, I was able to order an additional Nintendo Switch from the Nook Stop. Check the catalog of furniture you’ve obtained - it should list the Nintendo Switch for 29,980 Bells.

I haven’t purchased it myself, so I can’t say for certain that you can buy multiples off of it. You can definitely buy an at least one additional, though, since I still have the first one in my house.

At the very least, it's possible to order the ACNH Switch from Nook Shopping.

I saw a post the other day showing Nook selling the Animal Crossing special edition Switch. I would expect that he can also sell the regular Switch.