Are you asking if you can have more than one form on the page at the same time? And, if so, you you expect them to go to the same results page?

If you are using the shortcode method, and you want one form to be a simple search text box, then the other form must also have a search box (even if you hide it with custom CSS). In effect, you have a small search form and a big search form, the small form is a sub-set of the big search form.

If this then directs to another (different) page, that can have ONLY the big form and the search results shortcode for the big form.

You cannot send data from both forms at once though. It is EITHER the small form or the BIG form. This will change in V3 of our plugin, when what you want to do becomes very much easier.