Although not an optimal solution, if you have a correspondent FReepmail you with a question, you could post it as a "caucus" and then invite the non-caucus member to participate in it. If you invite somebody, they won't get bumped off the thread, even if it is a caucus.
The other way to do it is to post a doctrinal point, label it "caucus" and then in your comment, invite any non-caucus members to FReepmail you if they would like to join the thread. And then give them an "invite" based upon that FReepmail.
(RM, if I stated policy incorrectly, please correct me)
I just consider it a shame that all of these hoops exist primarily because of arguments between groups who call themselves "Christian." But such arguments have existed for at least 1700 years. Even Saints find themselves in these types of arguments. Consider the First Ecumenical Council:
Merciful, wise and fearless, Nicholas was a true shepherd to his flock. He was cast into prison during the persecutions of Diocletian and Maximian, but even there continued to instruct the people in the Law of God. He was present at the First Ecumenical Council in Nicaea in 325, and, in his zeal, struck Arius with his hand. For this act, he was removed from the Council and from his episcopal duties, until some of the chief hierarchs had a vision of our Lord Christ and His most holy Mother showing their sympathy with Nicholas.From St. Nicholas the Wonderworker, on the Coptic Orthodox Church Network site
The caucus format is not ideal for pursuing questions by non-members because if the non-member beliefs appear on the table then the caucus tag will be challenged by those not invited. Both the one asking and the one answering must be careful not to speak of the non-member beliefs.