DIVs are block level tags that can be nested.
Try assigning a class to BODY, and using the same class with the nested DIV.
If it doesn't work, there may be some precedence in the other class attributes that remain more significant. You may need to use:
!important ;
to override. Also, check syntax on the rest of the page, as "faulty" syntax can cause interpretation breaks.
cheers,
Torben