To have a progressive property tax schedule, don't you need the progressive scale to apply to the whole portfolio of holdings? It doesn't make sense to me for

To have a progressive property tax schedule, don't you need the progressive scale to apply to the whole portfolio of holdings? It doesn't make sense to me for it to be applied per-property as this just creates a loophole to sub-divide property titles. Why should one person be taxed less to own many small properties than someone owning a single large property of the same total value? And if so, how does this get applied to corporations and REITs? Do they get taxed out of existence, or do their holdings get apportioned to individual shareholders and included in their personal portfolio, so that individual progressive schedules are applied to each portion? It seems unlikely to me that you can construct a sound set of rules for this that are workable (no glaring loopholes) and appreciably different from a progressive wealth tax, which might be much easier to formulate...