Yes, you need that third table and it's called a Join table in database parlance.
cases::caseID = case_inquiry::caseID
Inquiries::InquiryID = case_inquiry::InquiryID
Here's a download link to a demo file that matches "contracts" to "companies" in exactly this fashion. Note how a portal to the join table is placed on both the contracts and companies layouts in order to link the records.
Thanks so much, I'll try that out.