Here’s the guide you have to follow if you want to have three full fireteams into Destiny: The Taken King’s Court of Oryx. First, use local random players in your lobby and message/party invite them, then invite your friends.
You just need two or three separate fireteams to meet up in one lobby and get lucky enough to have them respond to you.
From what we’ve seen, thanks to this method people on Reddit have knocked out roughly 10 Antiquated Rune fights in the Court of Oryx because they had coordinated people on one Xbox party chat.
Use your fellow Guardians but, of course, remember proper etiquette.