I don't think private security needs any police powers, however limited, and I don't think they probably want them either. As it is, they are now exempt from things like illegal search and seizure. If they were to be given police powers that could and probably would change in a heartbeat.
In KY, there is a position known as a Special Local Peace Officer which is what gated communities and large corporations can make their private security staff. They basically have powers of arrest on the property they are hired to protect. They can pursue off property only for a felony offense.
"If you're not a liberal when you're 25, you have no heart. If you're not a conservative by the time you're 35, you have no brain."- Unknown (NO...it wasn't Winston Churchill!)