In any collaborative effort, there is a chance that several people want to lead. The important part is identifying a leader and creating a team who will work together.
The challenge is when different groups do not want the same leader and communication is stifled as a positioning tactic to gain authority. You can navigate this by listening to the group, making sure everyone is heard, and ultimately making a decision with the best intentions for the collaboration in mind.
In the end, some people might not be happy and if you have done your due diligence as the leader, accepted mistakes, you can rest easy knowing you did your part.