Ideally, your approach is right but it would not guarantee you to get the best for your benefits.My suggestion is that you also need to think about two things below 1) If some agents are bragging or bluffing 2) If your mind is peaceful when you have better or worse quotes No matter at which side of table we are sitting, we do not want to be greedy . Otherwise, we lost balance and life will not be a happy one for us.