The biggest key for conversations with more than 2 RPers is for everyone to be on the same page for how the conversation will flow. Everyone just replying in whatever order is fine, when all RPers agree that they are fine with it. A posting order typically is the best solution, but it does not have to be the only solution. It depends on what each person prefers and how the flow of conversation happens in the RP. Sometimes the conversation naturally flows in a way that requires changing up the order. And if someone is unable to post for a certain length of time, check with them to know if they are alright if the conversation continues while they’re gone.
As long as each RPer agrees, a three way conversation can follow a specific order, or be done some other way.