It’s not possible with Dante either, the example you provided of Dante was asking how to get the cart in the top header, which it has, then it has a left area for text where you can add social icons.
If you want to add the supersearch to the top header but also have cart, links, social icons etc then you’ll have to make customisations to the theme, which I’m afraid is beyond our scope of support. While we’d love to be able to support every customisation request, we simply don’t have the time. We recommend that you seek a freelance developer if you need that functionality, potentially from one of the below resources:
https://codeable.io
Home
http://www.microlancer.com
Hope that helps.
– Kyle