If you want to keep it to the original style 2 cylinder engine then, bottom end strength is going to be the limiting factor.
Lets say we're using that 1000cc capacity, and if you say you're going to replace the head with a modern style OHC 4 valve head, then you should have the breathing and detonation resistance of a modern engine. There's plenty of road going, every day reliable engines making 100hp/litre, think Honda K series. So if your 1 litre engine could have a head with those characteristics and the right cam it should be able to make 100hp. If you venture into the world of motorbikes, then if you can rev high enough there are bikes you can walking into a show room today making 200hp/litre.
Once you add forced induction to that, just think the modern standard Abarth 500 engines will do 250hp with the right turbo, so thats 180hp/litre. And thats a road going engine that will do thousands of miles and have sensible service intervals. Nissan skylines and Toyota Supras can be modified to over 1000hp, so we are talking 300hp/litre and more.
So when you look at it that way, the real limit is not the top end or the breathing. The issue is in the bottom end strength, which as mentioned by
@the hobbler, is not always an easy thing to fix as there can be unexpected consequences, and the limit of how much heat the air cooled engine can dissipate.
Not to say you can't make your own bottom end, or do a water cooled conversion, but when does it stop being a 500 engine, and when would you be better off, again as
@the hobbler mentions, just bolting a different engine in!
Interesting to hear your story
@Toshi 975 of the turbo 126. When the crank design means revving high like a motorbike is not an option to make power, then forced induction does seem the obvious route. When you look at engines like this:
https://www.dangelomotori.it/prodot...n-testa-per-fiat-500-f-l-r-e-fiat-126-depoca/
€12k of OHC converted race engine, ,making 65-70hp. To make 100hp with the turbo is a good chunk faster than that! And in theory could be made much more 'usable' and tame than the 700cc racing engine would be.
These are all dangerous thoughts on cold dark winters nights, especially when I've got a good chunk of the parts I'd need to turbo my 500 sat in my shed...