Be assertive
It might sound contradictory that you can be empathetic and assertive, but one doesn’t exclude the other. Understanding the other person’s position does not mean you will allow them to be aggressive.
Keep your voice low and steady. This will show confidence and will not spur the other person into trying to talk more loudly than you.
Stand your ground, and don’t allow the person to monopolize the discussion. Speak out on your opinion.
Remain respectful, and ask for the same respect in return.
If the level of aggression begins to increase, respond with more force and assertiveness to show that your tolerance is decreasing.