Hi Cromers -
You've got a couple of options here, but they'd all take a similar approach.
If you're using a single collection for all the websites, you'll need to pass a scoping operator along with the user's query. Something like:
/s/search.html?collection=all-websites&query=QUERY&scope=website1
The value of the 'scope' parameter would need to be set by the calling site's template. For example:
<!-- Multi-website search -->
<form action="/s/search.html" method="GET">
<!-- Value of scope determined dynamically by calling website -->
<input type="hidden" name="scope" value="SCOPE">
<input type="hidden" name="collection" value="all-websites">
<input type="search" name="query" value="">
...
</form>
See also: http://docs.funnelback.com/url_scope.html
If you're using one collection per website, you'll need to alter the value of the 'collection' parameter on a per-website basis:
<!-- Single-website search -->
<form action="/s/search.html" method="GET">
<!-- Value of collection determined dynamically by calling website -->
<input type="hidden" name="collection" value="COLLECTION">
<input type="search" name="query" value="">
...
</form>
Finally, if you're using a multi-website collection, but no easy URL patterns are available for scoping, but you have metadata present in the pages to indicate the site name, a metadata-scoped search would be appropriate:
<!-- Multi-website search -->
<form action="/s/search.html" method="GET">
<!-- Value of metadata scope determined dynamically by calling website -->
<input type="hidden" name="meta_A_sand" value="SITE NAME">
<input type="hidden" name="collection" value="COLLECTION">
<input type="search" name="query" value="">
...
</form>
You'd need to ensure that your collection had a corresponding mapping for 'A' in metamap.cfg:
See also: http://docs.funnelback.com/query_operator.html
A,1,site-name
All of these calls should be easy enough to test in isolation - the component that I'm not able to advise on is how you'd configure your CMS (presumably Matrix) to alter the value of collection/scope/meta_A_sand based on the calling page.