Vico Magistretti/Arcadia table refinish  

Here are the pictures...

Josh,
I trash picked the same table worn and faded original finish and am utilizing a coworker who hobbies in fiberglass boat repair to rehab it
Once I am finished I will let you know

The first thing is to asses the condition of the table why it was painted over. Most of these early all plastic furniture were assumed invincible by many and were left outside but they were not. Like Kartell, Artemide during that time also used a type of plastic with a very shiny surface which can be buffed to shine like new with plastic polishers. Unfortunately when exposed to sun, rain and snow, the once shiny surface turns dull and a bit gritty that's why some painted it to make it presentable but paint on plastic will wear out too eventually.
If your table was painted black just because someone did not like the white plastic then you might be able to restore the surface by removing the paint, use caution whichever method you choose. If the surface of the white plastic is in decent condition, then you can use plastic polish products to remove light scratches and buff it to shine.
Plastic furniture from this period to be desirable should have the original (unpainted) surface. I don't know if you know what type of plastic your table has but the Selene chair also by Vico Magisretti for Artemide uses a compression molded plastic called Reglar, a fiberglass reinforced polyester.

Thanks Amazake and minimoma, I appreciate the help! I think I will try to carefully sand it down and polish. Ill let you know how it goes.
Josh

Based on the provided photos showing some of the paint stripped off, It looks like the original finish is not in good shape. I'd take it to a boat or fiberglass body specialist and have it refinished. Good find!