Learned a Three-Way Conversation Technique

When talking one-on-one with someone and a third person approaches to join the conversation, I should finish saying what I am planning to, to the first person. I should let the first person reply to what I said and if they don't include the new person in that reply, I should include the new person myself in my next reply.

This respects the person I am first talking to by concluding or continuing a subject and still makes the third person feel included.