I have worked on a project that had interests from multiple departments. For the most part the goal is that the aspects controlled by each department will not overlap and cause confusion. Sadly, this is just not true for how the real world works. I have had problems where something as simple as the maintenance manager and engineering supervisor not being able to agree on how often air filters should be cleaned in an air conditioner. The concept is trivial but often it can become a power trip between the two departments. My suggestion is to always listen to your direct supervisor. The person directly above you will hopefully defend you on disagreements. You never want to seem like you are going above your supervisor or go against them unless you personally believe the opposite opinion. I believe projects should always have one direct manager but sometimes you are forced to respond to more than one.