Multiple stylesheets

I am having problems with my wordpress theme, it has more than one stylesheet, it has a drop down menu which displays further options to the user. The link is: https://www.legalface.co.uk/blog/
I am trying to use a different stylesheet apart from the main style, it is located in the same theme directory and refernced, it has been referenced in the header, is there a specific way or standard method which needs to be used to apply more than one stylesheet for a theme?

Any help would be of use, thanks in advance.