So, if you want to include another contact in the conversation, you have to create a new group message (MMS group) that includes all the existing members plus the new contact you want to add. Essentially, you're starting a new group chat with the same people as the existing thread plus the additional contact. Here's how you can do it: More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.