We limited to 3 only because the design didn’t allow more in that position.
You can use the Header Widget area and add more social icons in there. You can use FONT AWESOME icons to create the links. In our demo http://wpestatetheme.org/ we use the contact info in there. But you can add more things. You just need to add TEXT WIDGETS and add in there the html code for fontawesome+link. You can create this in a page using the FONT AWESOME shortcode.