There are two ways of which I know. If it is a new conversation you are starting from your own inbox page, the conversation starts with a blank as to whom the message will be sent. Simply list the intended recipients, separating each with a comma (Minstrel, rhduke, Wreybies, etc.) If the conversation is one already in play and you want to invite someone new to it, go into the conversation and look over to the right under where your own badge information is. You'll see an area marked Conversation Participants. At the bottom of that area you will find Invite More. Click that. All of this assuming you are the originator of the conversation. If it was a conversation sent to you and you want to invite others, that is only possible if the original sender clicked the Allow anyone in the conversation to invite others box. If that was not clicked, you will not be able to do the aforementioned because the conversation has been sent as private.
In case you meant starting a new conversation, it's worth noting that New Members can only send to either one or two recipients, I'm unsure. As you move up the user group ranking to Member, Senior Member, Contributor, Supporter, etc., the number of people you can send PMs or "Conversations" to increases. This is to combat PM SPAM and advertising (which should be reported).