Move mini cart in second container

I’ve moved some elements through default.xml file. One of those elements, the top search, is moved.

At desktop it’s into the right position however not on mobile view. I’m wondering if it’s possible create a new container and to place the top search in a second container so I can hide one (with css on mobile) and display the other one.

If not possible; All information regarding responsible Magento design is welcome. 🙂