People can own multiple residencies, they just can't sell them at more than 3-5% profit. Corporations can't own residencial buildings if they are single family units but for multi-family properties, so long as it is being offered as rent/lease/purchase that should of course be allowed. I was focusing more on single family units but you are right to highlight that.
That would seriously restrict supply because once people bought a house with the intention of renting it out they would never sell due to the price control. Just like an entailment, this property can never leave the family line.
