If it's 2 element, it's not an omni... Just the driven element by itself would be an omni; AKA a full wave loop. If you were after something like that I would just put up a squalo.
http://www.freqtester.com/_mgxroot/page_10760.html And, no, stacking would not help... just use one.

Not sure what you are after as I have never worked the ISS, but you might take a look at my comments in another recent thread about omni versus directional antennas for satellites. However if this is for "unmanned" monitoring where you won't be there to adjust the rotor, then, yeah a squalo or other omni would be a simple choice. Otherwise you might want to look at an eggbeater or Texas potato masher type antenna. At 2 meters, you can get away with a lot more than you would if UHF were involved.
But to directly answer your question, the problem with the quad is that it would be directional straight up. And the ISS will rarely fly directly overhead and even when it does it's only there for mere seconds. (As in less than 60.)
73, Kevin N4UFO