you can add an hidden filed to your search form and include a different template based on that:
<form role="search" method="get" id="searchsupport" action="https://wordpress.stackexchange.com/">
<label class="screen-reader-text" for="s">Search for:</label>
<input type="text" onfocus="if (this.value == 'Search')
{this.value="";}" onblur="if (this.value == '')
{this.value="search";}" id="s" name="s" value="search" class="search-form round">
<input type="hidden" id="searchsubmit">
<!-- this is the magic field --->
<input type="hidden" name="custom_search" value="1">
<input type="hidden" name="post_type" value="software, documents" />
</form>
then in your theme’s search.php at the very top add:
if (isset($_GET['custom_search']) && $_GET['custom_search'] == 1){
include('custom_search.php'); // change it to whatever template file you would like to use
break;
}