"Private equity" isn't a monolithic structure that can be easily defined. It's just private companies with an exotic corporate structure. You can't really target them because you will target other private businesses in the process. What you can do is regulate their behavior so that a lot of their financial schemes are no longer profitable. Like, you shouldn't be able to buy a hospital and then create a shell company to lease it back to itself while investors pocket the rent. PE finds creative ways to stiff banks and consumers with financial engineering and that's what needs to be addressed.