Would Increasing Property Tax Rates on Subsequently Owned Properties Make Housing More Affordable?

To discourage the hoarding of land and properties, what if property tax worked similar to income tax brackets, with property tax being charged at a higher rate on subsequently owned properties? Alternatively, what if brackets were based on total acreage, value, or a combination of the two?

I don't believe this has been tried before, although there are similarities in vacancy taxes or taxes on non-owner-lived-in properties.

What would be the downsides? Could it effectively make housing more affordable for first time homebuyers? What could the additional tax revenue be used for, such as grants for first time homebuyers? Would tracking property ownership for a system like this be viable? Would it just further raise rent prices as property owners try to offset costs, or would it allow for multi-property owners to be edged out of the market due to higher costs compared to single or dual property owners, thus freeing up housing supply?

Edit: The ceiling for the first bracket would likely have to be at <5 properties or something. Or perhaps at a total value 3-5x the state's average cost of a home. Those are also just arbitrarily selected numbers though.