Can't say I know bluestacks well, aside from the fact that it's a piece of shit for trying it back then. But I've done it on 2 different s4 phones, both unrooted.
I've also done it with andy on PC (http://www.andyroid.net/), which I'd recommend using over bluestacks any day. You can also try droid4x (http://www.droid4x.com/) which I've heard works fine as well. They are both VBox wrappers so you can't use both at the same time (probably let alone installed at the same time either but don't quote me).
I've also read about someone running bluestacks and droid4x at the same time if you have a killer PC, but I have no desire to test it myself.