[bartelby]

Would look into different research regarding managing up, down and across and persuasion more generally. Robert Cialdini has a classic book called Influence I would highly recommend. I think at the management level you're describing, managing disagreements is often about trying to create internal alliances to advance whatever project/policies/changes you think are in the company's best interests.

It also might be that your company has grown to a point where not everyone's self-interest is aligned with the company's best interest. Would recommend Loonshots by Safi Bahcall which explores that idea quite a bit too.