How to separate select emails from a thread

I like using Threads, to keep repeated exchanges together. Today, I selected one of my emails, then Edit as New, to edit and send some of the content to a couple others, independent of the thread. but now, those emails to others are linked to the initial thread with the original recipient. I do not want them to be linked to that conversation thread, but instead for them to be in their own thread if a continuing email exchange occurs with these. I do not want to remove them from history, but rather to merely break the existing link to the thread involving a totally unrelated recipient.