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Not saying it can't be done, but it will require some modifications. The GM Performance serpentine system (I assume it's what you're asking about), uses a long water pump where the Corvette uses a short water pump. It will put the fan closer to the radiator. The whole system sits further forward than a stock C3 belt/pulley setup, and you'll have to modify your fan shroud as well. You'll also require a reverse rotation fan and fan clutch.
If you go to an electric fan setup you can eliminate the need for fan shroud modifications since you won't need the shroud at all.
There may be some other problems, but can be worked out. You'll have to decide whether it's cost efective to do so. You might look at some serpentine systems like March, Zoops, Billet Specialties, etc. They're much more expensive than the GM, but they have setups that are more compact and will fit within the width of the valve covers and no higher.
I just put on a setup from an 88 vette and it went on with no problems. You will need to drill a second bolt hole in the front of the passenger head and use thin SS washers to shim the brackets. If you get ALL the hardware it will go on no problem. I also went electric on the fans and deleted the shroud, WAY cleaner.
The Long pump in reverse rotation is required as stated by Roughrider.
The systems from March, Billet, Zoops etc were way too $$ for my budget
Go w/ a C4 Serp system. Most of the pieces can be picked up pretty cheap on ebay. When I was looking for one, most of the Vette recyclers nearby wanted $300 to $350 for everything. You will no doubt want to get a smog pump eliminator for a C4. They can be picked up used as well. Check the C4 parts for sale in the forum.
I believe the GMPP setup is the same as an F-body TPI setup. It will work with electric fans. I used a C4 setup on mine with an air pump eliminator from Breathless Performance. It fits great. The 2 main differences in C4 setups is 84-85 use an alternator that is similar to the 69-82 alternator and plugs right up. 86-91 C4 use a CS130 alternator that to be kind has had some reliability issues. You could swap in a CS144 that is much more reliable. The other difference is the a/c compressor. 84-87 use an R4 compressor like the 76L-82 C3s. 88-91 use a Nippendenso compressor that is very efficient. Buy the air pump eliminator to match the alternator.
I have a late-80s Camaro serpentine in my 77, it fits fine. As long as the ZZ4 uses the shorter passenger car brackets and not the enormously tall truck brackets, it should fit fine.