How to make different motivational models in one cross functional to become friends

Let's imagine a situation/problem - my personal, overthought about, overfelt, solved... IT company divided into freestanding departments, some of the departments are divided into conditionally independent sub-departments. Non-trivial topology ...

In every department there is a motivational model used visibly on non-visibly... there is no common motivational model in the company... cross-functional project development, Agile, Scrum, Kanban, their combinations... For clarity (and to be more dramatic) let's take the project as example: PM, Web Front End Development Department Manager, Java Backed Development DM, Manual QA DM, QA Automation DM, DevOps DM. How to organize effective team work? How to solve potential interests conflicts instead of trying to use common motivational model ...? Answers to that and other questions we will try answer from practical and academic-theoretical point of view in the course of our report-dialogue.