You've got to have something to invest it in, if you set up a business you need an office, could be the same address as the house. But that will look suspicious, which is why you need an immigration consultant who has dealt with these applications before as they will know all the pitfalls.
I met a couple from the
UK in Orlando a few years back who had opened a B&B and they lived in it, they didn't tell me what visa they had, but they weren't LPRs, so I assume it was E-2.
The problem is if you have kids, a friend of a relative of mine had E-2 and they lived in Florida and had an interior decoration business, but it wasn't really practical to stay forever because their son wasn't going to go to college (couldn't afford full tuition in the US as he would have been an international student) and he had no legal status once he was grown up. His only real relative overseas was an aged grandmother he didn't get along with so they decided to give up on it.
I guess the logic is if you do it this way, have your kids *after* you move because then they get US citizenship.
Steve.