Given the Southern/Eastern Province Kings are also due to come in, both teams would go into the SA conference, increasing it to at least 7 teams. Either 3 conference structure would remain, or the Aus/NZ conference could amalgamate into a Pacific conference. Since there would be a different number of teams in each conference, SANZAR might need to respond by adding more byes/rounds. Under a 3 conference system, Aus and NZ could continue to play all teams H&A within their conferences, but the SA/Arg conference might only be able to play all teams once, and two of the other 6 teams twice. SARU would not mind, they opposed the H&A concept as it duplicated matches in the Currie Cup.
AUS - NSW, QLD, ACT, Rebels, Force
NZ - Blues, Chiefs, Canes, Crusaders, Highlanders
Atlantic - BA, Stormers, Kings, Sharks, Cheetahs, Lions, Bulls
So in that pool, BA might play other teams once, but say the closest teams (Stormers and Kings) a second time. Similarly, the Bulls might only play Lions and Cheetahs a second time. Critics might say that the schedule might not be even for different teams, but neither is NFL, another geographically large competition with many teams. The cream will rise to the top.
I'd believe the players and competition overall would be better off with a reduction of two regular round games (leading to 14 regular round games), and an increase to a top 7 finals knockout.