There are at least a couple big turbo options that will work on the 124. I have been getting some questions about this, so I thought I would write a quick explanation here.
I want to start off by saying that in order to really take advantage of an upgraded turbo you will need quite a few supporting modifications, some of which don't yet exist for this car. Additionally, upgraded turbos are probably the single mod that's most likely to create a warranty issue. This is a mod typically done after the owner has upgraded other things and the car is nearing the end of its warranty period. So in my view talking about upgraded turbos at this time is getting the cart before the horse, but the information may still be helpful.
There are currently two proven bolt in turbo upgrades for these engine. They are the Garrett 1752 and the Gpop upgrade to the factory's GT1446 turbo.
The stock turbo starts to run out of breath around 220whp and it becomes inefficient. You may get a little more out of it, but probably not too much more. The 1752 on the other hand can generate quite a bit more with 270whp+ attainable with off the shelf supporting mods. (again, not all of which are currently available for the 124)
Let's look at the Gpop upgrade. It's available from NGEN Customs and Performance. It's a reworked stock turbo and appears stock externally. Internally it's seriously reworked.
Here is the GPOP turbo from NGEN:
You can buy it or find more information here: http://shop.ngencustomsandperforman...by-G-Pop-Shop-Turbo-Specialists-NGENTURBO.htm
The Gpop upgrade has some advantages over the 1752. It's a true bolt on, since it is the stock turbo externally it won't normally raise any eyebrows at the dealer or in typical inspections. It can make use of the common 1446 wastegate and diverter valve upgrades and connects to available intakes. It will connect to the stock downpipe, although I would strongly suggest a higher flowing downpipe, which doesn't yet exist for the 124.
I haven't used this upgrade myself, but I have several customers who have and by all reports it performs as advertised. Bryan at NGen is a top notch guy. He also works on Fiats so he can install this, or about any other mod for you if you live in the Houston area.
At Eurocompulsion we sell and use ATP's Garrett GT1752. This is the bigger of the two turbos and it's capable of efficiently providing the 124 engine with over 30 pounds of boost. Our off the shelf tune for this turbo runs 29psi and with supporting mods puts out just over 270whp. However there are some downsides vs the Gpop unit.
Here is the ATP GT1752
The 1752 requires a V5 intake, which is basically a V4 with a larger outlet where it connects to the turbo. It will also require different oil and coolant lines. For the 500 Abarth we have a kit that includes those lines, but since I haven't put it on a 124 yet, I don't know if they would fit. So expect to need 2 coolant and 2 oil lines to install this on a 124. The standard diverter valve will not fit, nor will it work at the boost levels needed to take advantage of this turbo. You will need the Forge diverter valve, no ifs ands or buts.
The 1752 is larger so that means it has a slightly higher boost threshold, about 150rpm higher than stock. That's not much, most won't even notice it and to a good driver it won't matter for performance, but for some it's a drawback. Of course once the boost is up, it gives more power per pound of boost and has higher limitations.
You can buy it here: https://shopeurocompulsion.net/collections/abarth-engine/products/atp-turbo-garret-1752-upgrade
Now, there is also a Gpop upgrade available for the 1752 but I haven't explored that at all. Clearly it would outperform the standard 1752.
It's possible to go with an even larger turbo, but in my view the downsides start to heavily outweigh the pluses. The 1752 and especially the GPop 1752 can put out so much power you will already be in danger of breaking things (at least in the 500 and probably in the 124) so why take the sacrifice in low end power and response if you can't fully exploit the potential at the high end? That's the reason we use the 1752 and not something even larger.
I hope all this helps.
Greg
I want to start off by saying that in order to really take advantage of an upgraded turbo you will need quite a few supporting modifications, some of which don't yet exist for this car. Additionally, upgraded turbos are probably the single mod that's most likely to create a warranty issue. This is a mod typically done after the owner has upgraded other things and the car is nearing the end of its warranty period. So in my view talking about upgraded turbos at this time is getting the cart before the horse, but the information may still be helpful.
There are currently two proven bolt in turbo upgrades for these engine. They are the Garrett 1752 and the Gpop upgrade to the factory's GT1446 turbo.
The stock turbo starts to run out of breath around 220whp and it becomes inefficient. You may get a little more out of it, but probably not too much more. The 1752 on the other hand can generate quite a bit more with 270whp+ attainable with off the shelf supporting mods. (again, not all of which are currently available for the 124)
Let's look at the Gpop upgrade. It's available from NGEN Customs and Performance. It's a reworked stock turbo and appears stock externally. Internally it's seriously reworked.
Here is the GPOP turbo from NGEN:

You can buy it or find more information here: http://shop.ngencustomsandperforman...by-G-Pop-Shop-Turbo-Specialists-NGENTURBO.htm
The Gpop upgrade has some advantages over the 1752. It's a true bolt on, since it is the stock turbo externally it won't normally raise any eyebrows at the dealer or in typical inspections. It can make use of the common 1446 wastegate and diverter valve upgrades and connects to available intakes. It will connect to the stock downpipe, although I would strongly suggest a higher flowing downpipe, which doesn't yet exist for the 124.
I haven't used this upgrade myself, but I have several customers who have and by all reports it performs as advertised. Bryan at NGen is a top notch guy. He also works on Fiats so he can install this, or about any other mod for you if you live in the Houston area.
At Eurocompulsion we sell and use ATP's Garrett GT1752. This is the bigger of the two turbos and it's capable of efficiently providing the 124 engine with over 30 pounds of boost. Our off the shelf tune for this turbo runs 29psi and with supporting mods puts out just over 270whp. However there are some downsides vs the Gpop unit.
Here is the ATP GT1752

The 1752 requires a V5 intake, which is basically a V4 with a larger outlet where it connects to the turbo. It will also require different oil and coolant lines. For the 500 Abarth we have a kit that includes those lines, but since I haven't put it on a 124 yet, I don't know if they would fit. So expect to need 2 coolant and 2 oil lines to install this on a 124. The standard diverter valve will not fit, nor will it work at the boost levels needed to take advantage of this turbo. You will need the Forge diverter valve, no ifs ands or buts.
The 1752 is larger so that means it has a slightly higher boost threshold, about 150rpm higher than stock. That's not much, most won't even notice it and to a good driver it won't matter for performance, but for some it's a drawback. Of course once the boost is up, it gives more power per pound of boost and has higher limitations.
You can buy it here: https://shopeurocompulsion.net/collections/abarth-engine/products/atp-turbo-garret-1752-upgrade
Now, there is also a Gpop upgrade available for the 1752 but I haven't explored that at all. Clearly it would outperform the standard 1752.
It's possible to go with an even larger turbo, but in my view the downsides start to heavily outweigh the pluses. The 1752 and especially the GPop 1752 can put out so much power you will already be in danger of breaking things (at least in the 500 and probably in the 124) so why take the sacrifice in low end power and response if you can't fully exploit the potential at the high end? That's the reason we use the 1752 and not something even larger.
I hope all this helps.
Greg