All you need is doing business, f.e. be partner in any ltd co. even if the Co. isn´t active. You have to pay yourself health&social insurance (some 150 euro I guess - this number use to be generated from minimum wage, now some 270 eur).
Friend of mine from Novi Sad who´s foreign Slovak has temporary residence in my house, he got permit to stay and can now freely travel in the Schengen area. If you have some slovak ancestors by any chance this could make it easier, as a foreign slovak all you need to get permit to stay is to have slovak adress.