There can be some good reasons to own multiple homes, so rather than banning it you tax it. That way people can still do it and the city gets more funding for allowing it. Those that can't do the tax will sell down.

A grandfather clause could be added, so that 'from now on' people can't buy more than 1 home. But there are plenty of less severe ways to fix the problem. A lack of solutions isn't the issue, anyway. The problem is that rich people who control countries don't want to fix housing problems, since they are often the people benefiting.