If you wanted to turn off different items within a family, you'd need to make as many sub categories for that family as there were parts.
Lets say you had a piece of mechanical equipment that needed access in one area. You could open the family item and add the lines indicating the access area required. Then if you go to Settings - Object Styles and then click the New button under Modify sub categories you could make a sub category called 'Access'. Highlight the new lines and go to Element Properties and select the name in the Sub Category Value box.
When the family is loaded you have the choice to change the visibility, line style, colour etc of the lines that comprise the 'Area' sub-category. But it will affect all instances of that family. One off, all off...