I agree with the sentiment that the first thing on the inner party's mind would be to prevent Trotsky's rise. If there was anything the core leadership agreed on, it was their shared hostility to him. Therefore, some sort of arrangement would have been worked out to push him away from any political influence he might have. And if the only way to avoid it is a Triumvirate or some kind power sharing agreement, at least in the short term, it will be agreed to. Stopping Trotsky would the strongest priority. However, had not inner party Democracy died already before Lenin? I wonder if a situation not unlike what happened after Stalin's death would happen here, some sort of power sharing arrangement between political powers in the inner party quickly emerges to block a hated figure from power, and eventually the shrewdest politician within that arrangement, or at least, the one with the fewest enemies within the party, eventually emerges as the effective leader of that arrangement, eventually forcing the other members out of power. I know, I'm massively simplifying to the point of mischaracterizing what happened after Stalin, and I realize that the situation I describe does not constitute a completely accurate description of what happened after 1953. However, I think that any power sharing arrangement is likely to be short lived. Either someone will come to dominate the triumvirate, presumably whoever engenders the least hostility, or there will be some outright conflict over the leadership once Trotsky is safely removed from a potential position of political influence. Someone will eventually emerge as the leader of the USSR, however I am not sure who would be likely to either be the most acceptable figure or best politician within a power sharing arrangement, or who would be in the best position to win a violent power struggle