Modification or addition of search style block elements?

Hello,

I’m wanting to implement a better UX version of search styling for Search Style 3 (or add my own search style search block element) for the Homepage Search Blocks.

Right now, Search Style 3 offers a standard dropdown option for selecting the category and a search text string input.

What I want to is to replace that with a Chosen JS version ( https://harvesthq.github.io/chosen/ ) and use the “Multiple Select with Groups” option where users could select multiple categories all from one dropdown then search for the text string they want. See the screenshot attached for the visual of the multiple selection.

I think it would be a much better option for people who want to search for something in multiple categories to cover all of their bases at once.

I of course want to do this via hooks so I don’t modify the core in any way possible.

Is this do-able?

Thanks guys