This is a difficult question to answer without more information about the three products. I would suggest you sit down with each team to understand their testing needs and move from there.
Integration of QA in work processes
In the company where I work there are 3 products: software, application and site - each with a different QA process. The question is how would you suggest integrating the QA process in different scenarios? Because there are tasks in which the QA man checks the task and there are those who "created" the task and checked whether it was indeed done at his request.
I look forward to your comments on this subject.