Yes, you should be able to have some other household own and run it. Just decide on a household who will own it, go to Manage Worlds and select and start playing that household. Cheat them enough money to buy it, and then buy it using the business tab in the bottom right corner of the screen. Now you can go back to Manage Worlds, mark that household unplayed again, and go back to playing your "real" household. Now that business should open when you visit it.