Even a body was avaible as a spare part so I guess it was possible to buy entire car in parts. But maybe it's about assembly kits that were sold to Egipt- I heard that cars were sent in boxes to Egyptian factory. Some FSO cars were also a kinda "custom built". Turbo kit for 1.5 was officialy avaible, also you could order some changes If you had money and knew the right people. For sure it was possible in FSM, my grandmother had a special built Polski Fiat 126p, it was stock actually but better made, better painted and they told me that engine was better than in any other 126p they ever had, and they had 4.
You could also buy after tests cars, (even after crash tests). I also heard that OBRSO (FSO development division) was swapping engines for special orders. Not to mention the fact that several prototypes were sold to private owners instead of going to museum.
Also there was a project of FSO Kit Car in early 90ties but it never came out.