Catluvsssyou Your Sim can only own one business* at a time. Households can own multiple venues, because each Sim in the household can own their own business - and you can also reassign which lot your business is associated with if you want to move it. I'm not sure whether or not you can run a single business on multiple locations, like a chain - I haven't tried yet.
*Edit: one small business. If you have Cats & Dogs or Get to Work or Dine Out you can still buy those businesses without selling your small business.
