Apparently, you cannot do any changes to your work permit (you have to obtain a new work permit if you want to do changes) and cannot work under any category of work that is not prohibited (as long as you have a work permit) in Bangkok, as I was said by the Labour dept.(This is a new law as they said)
TLDR : Answer Summary
It is currently stated that changes to a work permit cannot be made without obtaining a new one, and one cannot work in prohibited job categories in Bangkok. However, it is also noted that adding an additional employer to an existing work permit is possible if the primary employer provides a letter of consent, as the work permit operates as a booklet allowing multiple employers.