For me, the ideal would be: whoever started the dialogue could "pass" the scene to a companion who is within range.
From the perspective of development and implementation of mechanics, I wonder if it's really that difficult to allow players to switch who is in the conversation?
I want to say I have seen this mechanic in a party based CRPG. Wasn't it Storm of Zehir (Neverwinter Nights 2 expansion)? Or was it something else?