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"Multiple properties" is SIX or more?! That is so many properties. In a housing shortage, rich fucks should have to sweat to keep even a single residence unoccupied, but consequences don't start until six. It's the right direction, but that is still so bad.
Every city should just pass big ol' pied-a-terre taxes. Property taxes for a property operated as a primary residence by the owner should be a low coefficient on the millage rate. Property taxes for places with long-term tenants who call it their primary residence should get a medium coefficient on their millage rate. Properties that are not a primary residence should get a huge multiplier on property taxes. And unoccupied homes should be so expensive as to force a nearly-immediate sale.
Rent payments up to some reasonable threshold based on prevailing rates should be tax deductible, ensuring most rents show up on the city ledge.
This helps make up for the fact that renting costs more than owning in a way that targets relief to renters instead of owners without creating crazy incentive structures where rich fucks start selling their own homes to an LLC they rent it back from or other nonsense. Individuals can declare their rent payments absent any action by the landlord; totally under-the-table rent should be very rare.
All real estate transactions that aren't resulting in a property becoming a primary residence should have a HUGE sales tax.
Properties operated as a primary residence should have significant leniency on permitting for infill development -- owners living in their own property should have development-by-rights permission to do things like build an ADU. Development led by members of the community infilling in their own community should have a SUBSTANTIALLY lower bar for permitting than development by outsiders.