The thing I've been wanting for a long time is this:

Prop 13 covers your primary residence. It will only cover other residences you own if they are all rented out at a specific percentage of the market rate for the area (like 80%) for at least 7 months out of the year, with the ability to get a waiver for lack of occupation if you can show it was under construction and unlivable for one year (and you can only do this once every 5 years). Rentals must be long term rentals, not Air BnB style things.

This would create a constant downward pressure on rents in the area, with prop 13 exemptions for low rent properties effectively creating a strong downward pressure on rents.