Referrals from current clients are completely different from referrals from referral partners. Getting referrals from your current clients require a different conversation, because they already know you, your product, and the benefits. One of the best I know at having the conversation is a friend of mine named Amy. She has developed a system that allows her to receive 10+ referrals per week from her current clients.
I asked her how she was getting so many referrals, when most people are happy with one or two per week. She told me not to be satisfied with just one or two referrals. "I used to get only one or two per week until I started expecting three or four from each person. Unless you make it a point, they don't know how many they are supposed to give you. After setting expectations clients usually just keep providing names of people that I can help, until I stop them."