Multiple search boxes?

I wondered if it was possible to have multiple search boxes on one page. The problem I’m running across is that the id‘s for the search box has to be “s” but I’d like to have another search dialog box on pages when a search returns no results, but it won’t validate with two items having the same id.
To see what I mean, take a look here:
https://elasticdog.com/index.php?s=abcd&submit=Go