Mac Mail Groups Conversations with Different Subjects

In Mac Mail's Desktop and iOS Client:

If I'm in an email thread (conversation), and I want to split off that thread to keep information seperate and private, I generally will rename the subject with the prefix "Private" when I reply. In that new version of the thread, I only include a different group of people.

Unfortunately, this then groups that conversation with the non-private version of the thread – even though the subject line is different. That means I have multiple threads going within a single conversation and the results are email chaos.

Anyone have a solve for this beyond turning off "Organize by Conversation"?

A better way to ask the question is perhaps: how do I split up a grouped conversation? Or: how do I fork off a new conversation?

I want my conversations/threads to say grouped by SUBJECT - not anything else.