Searchable custom fields in normal search layout

Hello,
im wondering if is possible and how I could display some searchable custom fields in the normal search area.
By "normal search area" I mean the search area displayed, for instance, in category view.

I'd a look on the documentation but I haven't found an answer.

Basically, what I need to achieve is to be able to let users to search by other two fields: a date field and a drop down menu. But I need that in category view, not in advanced search view. Is there any way to do that?

Thanks, kind regards.
Gregorio