The new Chop Shop is now live in game! Here's how it works.
The original 5 Chop Shop pieces can be used to upgrade your Chop Shop to different levels (power tools, cement blocks, etc).
There are 10 total levels, with each level unlocking a new car type and the ability of your Chop Shop to produce more parts.
At any rate, it starts off costing 5 of each type of car part for each level and this number increases by 1 per level (6 to get to level 3, 7 to get to level 4, etc).
There are a large variety of car types available at the Chop Shop. Here is a list:
Level 1: Random common car - 10 car parts required
Level 2: Random rare car - 25 car parts
Level 3: Tasmanian - 36 attack, 34 defense - 30 car parts
Level 4: CM Santiago R10 - 42 attack, 30 defense - 30 car parts and 2 Cuban Car Parts (guessing these drop from fights and jobs in Cuba)
Level 5: Rebel 2 - 40 attack, 45 defense, +5 stamina (not sure if you can collect +5 stamina each time you can collect a car - need confirmation) - 45 car parts and 2 bulletproof glass.
Level 6: Russian Dazatz 45 - 18 attack, 46 defense - 50 car parts and 2 Russian Car Parts
Level 7: Solar Flare - 34 attack, 34 defense, +5 energy - 65 car parts and 1 solar panel
Level 8: Thai XS Max - 45 attack, 35 defense - 75 car parts and 2x Thai Car Parts
Level 9: Trio Napoli - 47 attack, 23 defense - 95 car parts
Level 10: Red Angel - 16 attack, 49 defense - 115 car parts
Some more information:
Car parts drop randomly from all sorts of jobs and fights, as do the specialty items such as "solar panel" and "bulletproof glass". The specialty items seem to be rarer but still seem to be a random drop.
Additionally, each type of zone based cart part drops from its respective city (Cuban Car Part drops in Cuba, Thai Car Part drops in Bangkok, etc). These drop from random jobs and fights as well - you just have to be in the city.
You can also get car parts pieces simply by fighting and doing jobs. It would seem that the fastest way to upgrade your chop shop would be to repeat a low energy cost job in New York!