I have a question for you.
What percentage of Canadian homes are owned by a single person or family who has 3 or more properties?
What if I told you that number is so small that your argument is great rage bait, but realistically useless?
65% of residential properties in Canada are owned by the family that lives in them, another very large chunk is dedicated rental apartments, then there's a ton of second properties like cottages, etc., then of course there are people who have a second property for rental, but the number left remaining for people with a third property (for themselves or rental) is less than a couple percent of the total housing market.
Go ahead and implement that tax, it's not going to hurt anyone I care about, but if you expect any noticeable effect on the housing market you're not thinking logically about the situation.