Buying second homes possible ?

I have also purchased retail lots and used them as second houses. In my experience, only paparazzi tend to come onto the lot when the business is closed, but to be on the safe side, locking the doors is a good idea.
The other annoyance of using a retail lot as a house is that every item you interact with (and some that you ordinarily couldn't) has a "set for sale" option. If you accidentally click it when you're intending to open the refrigerator to get leftovers, it can disrupt your sim's morning routine.
I haven't tried using a different type of business lot. Maybe a vet clinic or restaurant would work better.

Without mods. If you have get to work you can technically buy another home but as a business. I have done this. I didn't furnish it as a business but as a family home. However, you will have to lock all doors for household only as other sims will just wander in even though the business was closed.