Easily solved by not hitting people who own one property which is their primary residence.
I'd go easy on two-property people; some people need two places for various reasons, and they occupy both.
The tax rules can be crafted such that heavy penalties are imposed on people with three or more properties, and on house flipping activity.
Only reason you don't see more of that is because, doh, the rules are written by the rich. The politicians themselves or their rich chums are doing a lot of that speculating.