1. Scale property tax for number of properties owned. Double it per property owned.

i.e. own 2 homes, property tax for ALL homes owned doubles. Own 3 homes, pay 4x property tax. etc. Homes should not be hoarded. And corporations are definitely not exempt, except perhaps before first sale (i.e. they constructed the property) or demolition sale (buying multiple properties for demolition to be able to construct denser units)

2. Add or expand speculation tax (like the empty homes tax): it should be decently large, like at least 10% of the property's assessed value per year. However, it can be negated based on income tax paid by someone who lives at that location (as reported on their tax filing). There may need to be some additional reductions for retirees/seniors too.

Either way somebody's gotta live and work there to avoid the tax. No "students" owning multi-million dollar mansions.