This is an easy problem to legislate away, our politicians are just too cowardly to decommodify housing.
Of course this would be a giant pain of a workaround to scale, but for the non-mega corporations it'd probably work. I'm sure that the huge corporations owning large swaths of residential properties would figure out scaleable loopholes.
They could also add in a carrot, to reduce capital gains on sale of non-primary residences.
There are too many incentives currently to hoard properties like the damn monopoly man, so you need to start clawing away at them. Taxing the eventual sale just encourages people to not ever sell, so tax them for hoarding directly.
I'll be 90% or more own multiple houses.
Plenty of families out there own rental houses as an investment, which I think is a good thing. It allows people an alternative to investments like the stock market if they aren't into that, and it gives a path to turn labor into wealth through DIY maintenance, repairs, and improvements.
Plus it allows individuals to better manage situations like parents dying and leaving them a house that they may not want to sell immediately.
I mean in general the only possible solution is more housing ... which would mean
1) zoning up neighborhoods
2) make it financially interesting to convert properties and make them denser