First, spend the time to understand your own ego.
And, as you do that recognize you will tend to see yourself as less egotistic and possessing higher self-esteem than other people. At least, that’s the way most people view themselves, as compared with others.
Next, work to limit your judging of other people.
When you observe what you believe to be excess ego…you may be judging too harshly? Your judgement may be inaccurate? You may be unskilled at judging accurately?
Or, your judgement may be accurate.
Assuming your judgement is accurate – assuming the other person is showing an excess of ego – recognize you are seeing the other person’s reaction to fear. You probably will not be able to guess the fear. And the person with the big ego may not understand the fear that is causing excessive ego.
Recognize – your logic will not remove another person’s ego problem. Ego is not about logic. Ego is about emotion. And the underlying driver is fear.
Next, analyse the situation.
Situations have a major influence on people’s feelings and actions. The situation includes something that is triggering fear in the high-ego person. To the extent you can alter the situation you may be able to reduce/remove the thing that is triggering the fear.
However; the situational thing that is triggering the person’s fear could be very broad/general. For example, most people show signs of changed behaviour when they are under stress. And, the stressful thing could be as broad as ‘having to go to work...and be around people’.
Does the person have a large ego in all situations?
If so then do what you can to avoid the person…you will not change the person.
If the person only shows ‘large ego’ in certain situations then do what you can to avoid those situations or remove them. If, for example, you are the boss then you can influence the situation. You can influence when, where, and how interactions happen with the person.
Neither feed nor assault the other person’s ego. Be matter-of-fact, not emotional. Make sure your actions align with your personal values…not the other person’s.
Do not criticize or work to outmuscle the other person because that could push things into ‘bully territory’.
Diffuse the situation rather than escalate it.