If you put hot cholent on your plate.Can you add ketchup to the cholent on Shabbos.
R’ Moshe Feinstein zt”l writes about this in Igros Moshe, and he says that you can. His reason is since the ketchup was already cooked, even though we are stringent regarding bishul achar bishul, however in this instance it is coupled with another factor. The fact that the cholent is no longer inside the kli rishon. The poskim discuss whether a solid food that is no longer in the kli rishon, has the capability to cook. Although we are strict regarding this, however since there are two issues here, we can be lenient, therefore he says that it is permitted.
Igros Moshe O:CH 4 74 Bishul 5.