It depends on how you set them in your header. So something like this will work:
<link rel="old stylesheet" href="https://stackoverflow.com/questions/16913131/path/to/style.css" />
<link rel="newer stylesheet" href="https://stackoverflow.com/questions/16913131/path/to/style.css" />
<link rel="newest stylesheet" href="https://stackoverflow.com/questions/16913131/path/to/style.css" />
The last one will be picked up.
And an helpful link about stylesheets here:
http://www.w3.org/TR/html401/present/styles.html#h-14.3.2
See also: Precedence in CSS if the above doesn’t work for you.
Hope it is clear.