Suggestion for limiting search by membership?

I think I am posting this in right place, but I’m looking for recommendations for either theme or plug-in for a membership site.

In particular, I’m looking for a way to limit the number of searches/month by the level of membership: Higher level gets more searches.

I’ve seen plenty of membership plug-ins, but most are more focused on limiting the content, rather than limiting the searches.

Is there anything like this out there that someone can point me to? Thanks in advance