This requires an advanced theme customization you'll basically either need create a new second menu structure to hold the other sides items, or inject logic to split the existing menu among different elements in the header.
While it may be possible with just CSS tricks it's generally not worth it for the side effects that can cause.
And then theres accounting for the design adjustment to move the icons around.
If you need this customization then contact me by mail for services, Contact info in signature. ALWAYS please provide context, examples: store url, theme name, post url(s) , or any further detail.