The cost of this would just be passed on to people who rent rather than own, since the extra tax would apply to any property they could rent.

You could charge exponentially more tax based on the number of units rented. That way even if the cost is passed on, renters are incentivized to rent from small landlords.

Then you simply have a web of LLCs so that each corporate entity only owns a single unit.

Administrative costs are costs too.

Then tax and cap rent increases county wide on every building no matter when it was built or if a tenant moves out. Then again, I'm pretty far left on housing issues. In my ideal world, the rent formula would be:

monthy rent = 0.3(minumum hourly wage * 160 hours) * n bedrooms; with studios being n = 0.5

That way if landlords want to lobby for higher profit margins, the only way to do it would be to also ensure the working class can actually afford to supply those higher profit margins for the landlords.

Depends on the details - the tax could be paid by the occupants a bit like the council tax in the UK. And then discounts applied. Or by the owner if the property is unoccupied.