No, the easiest way to curb this is to make it easier to build homes so that supply is closer to the level of demand, not create even more policies that will reduce supply.

Controlling 11% of the rental market is not enough to manipulate it, and that's one of the most concentrated markets in the US if I remember correctly. It's not an actual issue. If those 3 companies are in fact colluding, use the existing laws against that to prosecute them instead of inventing more counterproductive policies.