You can get a line out converter that will splice the speaker leads on the back of your factory Head Unit. If you can find a wire diagram for the factory unit it will lay out what wires are for what channels. Just match the wires from your harness to the ones on the converter.
I have not done it on my JKU but in previous vehicles I have ran a few different systems off of the factory Head Unit with no problems using one. Depending on how many speakers you are hooking up you could be looking at anywhere from $15-$125.
I would recomment a simple Scosche 2 or 4 channel line out converter. Both are easy to find as close as your local Walmart for 15-25 bucks. They feel a little cheap but they WORK well and have never had an issue with either one. If you are looking to spend a bit more money the AudioControl LC6i and LC8i are options as well. These are higher quality units but will also run you a higher cost closer to the $120-$200 range. Any of these however will give you the required RCA outputs you need to hook up any system to your factory Head Unit.
Hope this helps a little. Keep us posted and good luck!
I'm sure Crutchfield would have some kind of an adapter.