I guess the best way to render it would be exactly like `<select>` when closed, but when opened there should be a search box where it'd normally show the first option.
Clicking search would call a javascript function, which could then adjust the set of available options via the standard DOM APIs.
Alternatively they could add support for a special element `<selecthead>` which can contain whatever you want, which would render fixed at the when the drop down is opened and can be interacted with like normal html elements. Then you could place your own search fields inside.