Inclusive search or search operators

When trying to search for “Brand Product” I will get the expected results, but when I search for “Brand Product Problem” or almost any other word I will get a “No results found” message. So I’m trying to figure out, how to get more inclusive search results. Is there a way to return results which does contain at least one of the search terms, or incorporated operators into the search query?

Ideally, I would need this to be done via the API.

Thank you for your guidance and help.