Does anyone knows what happens if changing, in a 2000 4.0 TJ, the factory reccomended PS fluid (the Mopar clear one) with an ATF 4?
I have changed my PS pump some times ago (with a sealed Mopar "remanufactured" one, bought from a dealer in Germany), drained the system, filled in with the Mopar fluid (stated in the operaton manual) and had almost the same symptomps as before (hard steering on the trail, whinning pump etc). Sending the pump back for a replacement/refund would cost me almost as much as the pump itself (plus that it was not installed in a Chrysler authorised garrage). Now, that's summer (and hot, more than 35 C) it got worse. Before buying another pump, I was thinking of draining the fluid and replacing with an ATF 4, to see if something changes, but I would like to know (if anyone could tell me) what can happen.

Yes that is OK as I have done that. Mopar stuff is extremely over priced for what it is. I just replaced my steering box with one from PSC and it has made all the difference. Just make sure when you drain the fluid and add new fluid do a little at a time and turn the steering wheel back and forth to get the air out. DO NOT START THE JEEP AND TURN THE WHEEL as this will cause the box to make loud screeching noises. The fluid will drain lower as more and more air comes out. Just have someone keep an eye on it for you while steering back and forth until its filled. Every now and then after driving check the fluid levels.

If I understand well, you have added the ATF after changing the steering box, right? I wonder what can happen if using the ATF with the OEM setup (pump and box)? I would like to test cheaper "fixes" before changing (again) the steering pump.
And, indeed, Mopar is extremely expensive (and I doubt that that's the real manufacturing cost). Here, in Romnaia, you can but a quart of Mopar power steering fluid for the 2000 TJ, for 25-28 USD, which I find outrageously expensive.