Best Practice on Changing Outerwear

We have employees that have multiple roles.  Some roles require a white coat/frock (handling raw materials) and others require a gray coat/frock (handling trash on floor, squeegeeing floors).  If an employee is wearing a white coat for handling raw materials, is it okay for him to put on his gray coat over the white, or should he take off the white coat first?  I prefer he take the white coat off and then put on the gray coat, but another manager is telling me an inspector once said it is okay to have both coats on at the same time.

take the white one off

Zero chance I'm leaving the raw processing coat on over a coat that could be worn for anything else.  I don't care what an inspector might've said, a braindead RA of this is a hard no.

Thanks for the responses.  Sometimes I am dumbfounded by the things people do.  To me, so many things are obvious, but to so many others, they think just because something has always been done one way that it is perfectly fine to continue doing things that way.

I have been told that 'over the white smock' was OK too, but I just don't like it.

shoot the inspector, he/she is wrong.